How is dividing a polynomial by a binomial similar to or different from long division?
Q. How is dividing a polynomial by a binomial similar to or different from the long division you learned in elementary school? Can understanding how to do one kind of division help you with understanding the other kind? What are some examples from real life in which you might use polynomial division?
Asked by chiko - Thu Mar 27 00:01:18 2008 - - 1 Answers - 0 Comments
A. Sounds like you typed an exact question you had for homework. Neat. They're the same. In fact, the long division you learned in elementary school is a special case of general polynomal long division for x assigned the value 10, eg. 1231 = 1 * 10^3 + 2 * 10^2 + 3 * 10^1 + 1.
Answered by Will - Thu Mar 27 00:11:55 2008
Q. How is dividing a polynomial by a binomial similar to or different from the long division you learned in elementary school? Can understanding how to do one kind of division help you with understanding the other kind? What are some examples from real life in which you might use polynomial division?
Asked by chiko - Thu Mar 27 00:01:18 2008 - - 1 Answers - 0 Comments
A. Sounds like you typed an exact question you had for homework. Neat. They're the same. In fact, the long division you learned in elementary school is a special case of general polynomal long division for x assigned the value 10, eg. 1231 = 1 * 10^3 + 2 * 10^2 + 3 * 10^1 + 1.
Answered by Will - Thu Mar 27 00:11:55 2008
Find a polynomial with integer coefficients and a leading coefficient of one that satisfies the given?
Q. Find a polynomial with integer coefficients and a leading coefficient of one that satisfies the given conditions. P has degree 2, and zeros 1 + i 5 and 1 - i 5. P(x) =?
Asked by Math - Tue Sep 22 16:54:24 2009 - - 1 Answers - 0 Comments
A. If x = a is a zero, then x - a is a factor. Since x = 1 + i 5 and x = 1 - i 5 are solutions, we have the following equation for P(x): P(x) = [x - (1 + i 5)][x - (1 - 5)] ==> P(x) = (x - 1 - i 5)(x - 1 + i 5) You can re-write this and get: P(x) = [(x - 1) + i 5][(x - 1) - i 5] This is a difference of squares, so we can get: P(x) = (x - 1) - (i 5) ==> P(x) = x - 2x + 1 - i (5) ==> P(x) = x - 2x + 1 - (-1)(5) ==> P(x) = x - 2x + 1 + 5 ==> P(x) = x - 2x + 6 Answer Verification: I hope that helps!
Answered by unknown - Tue Sep 22 20:24:30 2009
Q. Find a polynomial with integer coefficients and a leading coefficient of one that satisfies the given conditions. P has degree 2, and zeros 1 + i 5 and 1 - i 5. P(x) =?
Asked by Math - Tue Sep 22 16:54:24 2009 - - 1 Answers - 0 Comments
A. If x = a is a zero, then x - a is a factor. Since x = 1 + i 5 and x = 1 - i 5 are solutions, we have the following equation for P(x): P(x) = [x - (1 + i 5)][x - (1 - 5)] ==> P(x) = (x - 1 - i 5)(x - 1 + i 5) You can re-write this and get: P(x) = [(x - 1) + i 5][(x - 1) - i 5] This is a difference of squares, so we can get: P(x) = (x - 1) - (i 5) ==> P(x) = x - 2x + 1 - i (5) ==> P(x) = x - 2x + 1 - (-1)(5) ==> P(x) = x - 2x + 1 + 5 ==> P(x) = x - 2x + 6 Answer Verification: I hope that helps!
Answered by unknown - Tue Sep 22 20:24:30 2009
I've plotted a polynomial graph with R Square value in Excel. How do I find the significance value?
Q. I've plotted a polynomial graph in Excel. I added the stats box which shows the R Squared value for the data. How do I find the significance value for this R Squared value?
Asked by Ganders - Mon Nov 26 04:55:54 2007 - - 1 Answers - 0 Comments
A. Unfortunately, Excel doesn't carry distribution tables and can't give you the significance value for R, or any other parameter for that matter. You will need to construct Fisher's Z-transformation for R, which is easy to do, and then look in tables of the Normal distribution. The Wiki page below shows you how to do it. For a large sample N of points, say over 50, but the books say over 100, the standard error of R can be approximated by 1/sq-root(N-3). If the null hypothesis is R=0, then this value for standard error can give you a quick idea if R-squared is significant. For example: N=50 and R-squared calculated as 0.4 Then R=0.63 Std err R approx = 1/(sq-root 47) = 0.146 Two std errors = about 0.3 R exceeds 0.3, so there is… [cont.]
Answered by Victor - Sun Dec 2 17:56:03 2007
Q. I've plotted a polynomial graph in Excel. I added the stats box which shows the R Squared value for the data. How do I find the significance value for this R Squared value?
Asked by Ganders - Mon Nov 26 04:55:54 2007 - - 1 Answers - 0 Comments
A. Unfortunately, Excel doesn't carry distribution tables and can't give you the significance value for R, or any other parameter for that matter. You will need to construct Fisher's Z-transformation for R, which is easy to do, and then look in tables of the Normal distribution. The Wiki page below shows you how to do it. For a large sample N of points, say over 50, but the books say over 100, the standard error of R can be approximated by 1/sq-root(N-3). If the null hypothesis is R=0, then this value for standard error can give you a quick idea if R-squared is significant. For example: N=50 and R-squared calculated as 0.4 Then R=0.63 Std err R approx = 1/(sq-root 47) = 0.146 Two std errors = about 0.3 R exceeds 0.3, so there is… [cont.]
Answered by Victor - Sun Dec 2 17:56:03 2007
What is the relevance of the order of operations in simplifying a polynomial?
Q. - What operations are associated with exponents? - What is the basic principle that can be used to simplify a polynomial? What is the relevance of the order of operations in simplifying a polynomial? - When multiplying two polynomials, what fundamental property do you use repeatedly?
Asked by avonlady1971 - Wed Apr 15 21:03:46 2009 - - 1 Answers - 0 Comments
A. - Multiplication - Division. Parenthesis Exponents Multiplication Division Addition Subtraction is the order of operations. You still must follow these when simplifying a polynomial. - When multiplying two polynomials, what fundamental property do you use repeatedly? - The property that says you can multiply terms containing exponents by adding the exponents. I forgot what it's called, sorry. I hope that helped! :)
Answered by a La AkiLi - Wed Apr 15 21:13:37 2009
Q. - What operations are associated with exponents? - What is the basic principle that can be used to simplify a polynomial? What is the relevance of the order of operations in simplifying a polynomial? - When multiplying two polynomials, what fundamental property do you use repeatedly?
Asked by avonlady1971 - Wed Apr 15 21:03:46 2009 - - 1 Answers - 0 Comments
A. - Multiplication - Division. Parenthesis Exponents Multiplication Division Addition Subtraction is the order of operations. You still must follow these when simplifying a polynomial. - When multiplying two polynomials, what fundamental property do you use repeatedly? - The property that says you can multiply terms containing exponents by adding the exponents. I forgot what it's called, sorry. I hope that helped! :)
Answered by a La AkiLi - Wed Apr 15 21:13:37 2009
How do I show that a polynomial function is continuous at a point?
Q. How do I show that a polynomial function is continuous at a point? Would this be a proof? If so how do I prove it? Any helpful websites that are easy to digest?
Asked by Josephine - Tue Oct 28 01:58:34 2008 - - 2 Answers - 0 Comments
A. Is the function F(x) = x continuous everywhere? (Yes) Is the function G(x) = 1 continuous everywhere?(Yes) If f and g are continuous everywhere, is f+g continuous? How about f*g? (Yes, Yes) Note that 3x^2 = (x*x)+(x*x)+(x*x) Show that every polynomial is the finite sum of finite products of F(x)=x and G(x)=1 and hence continuous everywhere.
Answered by Michael E - Tue Oct 28 02:16:49 2008
Q. How do I show that a polynomial function is continuous at a point? Would this be a proof? If so how do I prove it? Any helpful websites that are easy to digest?
Asked by Josephine - Tue Oct 28 01:58:34 2008 - - 2 Answers - 0 Comments
A. Is the function F(x) = x continuous everywhere? (Yes) Is the function G(x) = 1 continuous everywhere?(Yes) If f and g are continuous everywhere, is f+g continuous? How about f*g? (Yes, Yes) Note that 3x^2 = (x*x)+(x*x)+(x*x) Show that every polynomial is the finite sum of finite products of F(x)=x and G(x)=1 and hence continuous everywhere.
Answered by Michael E - Tue Oct 28 02:16:49 2008
What is the flow for finding zeros of a polynomial function?
Q. I have the following directions and equation: Find all the zeros of the polynomial function and write the polynomial as a product of its leading co-efficient and its linear factor (hint: first determine the rational zeros). P(x)=x^4+x^3-2x^2+4x-24 I am not getting the order and answers I think I need. Please help. Thanks.
Asked by Charles - Mon Sep 7 08:49:50 2009 - - 1 Answers - 0 Comments
A. Use the rational root theorem. Where p is the constant term and q is the leading coefficient. factors of p: 24, 12, 8, 6, 4, 3, 2, 1 factors of q: 1 So p/q: 24, 12, 8, 6, 4, 3, 2, 1 Plug those values into your given function and see which ones give you a zero. You will see that the x = -3 and x = 2 give you zeros. Use synthetic division with one of your zeros to find the others -3 1 1 -2 4 -24 ___-3__6_-12_24___ 1 -2 4 -8 0 So now use x^3 -2x^2 + 4x -8 and x = 2 and synthetic division to find the others... 2 1 -2 4 -8 ___2__0__8_ 1 0 4 0 So now you have x^2 + 4 = 0 You can easily find the other roots by solving for x x^2 + 4 = 0 x^2 = -4 x = 2i So your roots… [cont.]
Answered by unknown - Mon Sep 7 09:04:21 2009
Q. I have the following directions and equation: Find all the zeros of the polynomial function and write the polynomial as a product of its leading co-efficient and its linear factor (hint: first determine the rational zeros). P(x)=x^4+x^3-2x^2+4x-24 I am not getting the order and answers I think I need. Please help. Thanks.
Asked by Charles - Mon Sep 7 08:49:50 2009 - - 1 Answers - 0 Comments
A. Use the rational root theorem. Where p is the constant term and q is the leading coefficient. factors of p: 24, 12, 8, 6, 4, 3, 2, 1 factors of q: 1 So p/q: 24, 12, 8, 6, 4, 3, 2, 1 Plug those values into your given function and see which ones give you a zero. You will see that the x = -3 and x = 2 give you zeros. Use synthetic division with one of your zeros to find the others -3 1 1 -2 4 -24 ___-3__6_-12_24___ 1 -2 4 -8 0 So now use x^3 -2x^2 + 4x -8 and x = 2 and synthetic division to find the others... 2 1 -2 4 -8 ___2__0__8_ 1 0 4 0 So now you have x^2 + 4 = 0 You can easily find the other roots by solving for x x^2 + 4 = 0 x^2 = -4 x = 2i So your roots… [cont.]
Answered by unknown - Mon Sep 7 09:04:21 2009
How do I find remaining factors of a polynomial based on this equation?
Q. Given the binomial, x-2, is a factor of x^3-6x^2+11x-6, find the remaining factors of the polynomial.
Asked by tinkerbellwantabe - Tue Mar 11 21:29:24 2008 - - 2 Answers - 0 Comments
A. divide x^3 - 6x^2 + 11x - 6 x goes into x^3 this many times: x^2 x^2 times (x-2) = x^3 - 2x^2 subtract that from x^3 - 6x^2 + 11x - 6 = -4x^2 + 11x - 6 x goes into -4x^2 this many times: -4x -4x times (x-2) = -4x^2 + 8x subtract that from -4x^2 + 11x - 6 = 3x - 6 x goes into 3x, 3 times 3 times (x-2) = 3x-6 subtract that, there is no remainder so (x^3 - 6x^2 + 11x - 6) / (x-2) = x^2 - 4x + 3 Now factor that binominial into (x-3)(x-1) Final answer: (x-1)(x-2)(x-3)
Answered by Steve A - Tue Mar 11 21:37:53 2008
Q. Given the binomial, x-2, is a factor of x^3-6x^2+11x-6, find the remaining factors of the polynomial.
Asked by tinkerbellwantabe - Tue Mar 11 21:29:24 2008 - - 2 Answers - 0 Comments
A. divide x^3 - 6x^2 + 11x - 6 x goes into x^3 this many times: x^2 x^2 times (x-2) = x^3 - 2x^2 subtract that from x^3 - 6x^2 + 11x - 6 = -4x^2 + 11x - 6 x goes into -4x^2 this many times: -4x -4x times (x-2) = -4x^2 + 8x subtract that from -4x^2 + 11x - 6 = 3x - 6 x goes into 3x, 3 times 3 times (x-2) = 3x-6 subtract that, there is no remainder so (x^3 - 6x^2 + 11x - 6) / (x-2) = x^2 - 4x + 3 Now factor that binominial into (x-3)(x-1) Final answer: (x-1)(x-2)(x-3)
Answered by Steve A - Tue Mar 11 21:37:53 2008
How do i find the total solutions to a polynomial equation, complex and repeated?
Q. The directions say determine the total number of solution (including complex and repeated) of the polynomial equation. The first problem is 4x^3-7x^2+5x-9=0. I just need to know where to start and what to do.
Asked by Aaron B - Sun May 20 22:08:58 2007 - - 1 Answers - 0 Comments
A. Normally you could figure this type of problem out by factoring it, but I can't easily figure it out. Can you use a calculator? If so, type that in to y= and then where the graph crosses the x axis on the graph is/are your answer(s). The most possible is 3 because that is the highest exponent.
Answered by Amber - Sun May 20 22:44:40 2007
Q. The directions say determine the total number of solution (including complex and repeated) of the polynomial equation. The first problem is 4x^3-7x^2+5x-9=0. I just need to know where to start and what to do.
Asked by Aaron B - Sun May 20 22:08:58 2007 - - 1 Answers - 0 Comments
A. Normally you could figure this type of problem out by factoring it, but I can't easily figure it out. Can you use a calculator? If so, type that in to y= and then where the graph crosses the x axis on the graph is/are your answer(s). The most possible is 3 because that is the highest exponent.
Answered by Amber - Sun May 20 22:44:40 2007
What is max number of critical points of polynomial with degree n?
Q. Let f(x) be a polynomial of degree n. a) What is the maximum number of critical points f(x) can have? For each n, give an example with proof of a polynomial having the maximum number for that n. b) Answer the same question with 'maximum' replaced by 'minimum'.
Asked by Ohhhhh heyy - Mon Apr 27 20:37:30 2009 - - 4 Answers - 0 Comments
A. A) n-1. Example is x^3-x, it has two. If you need multiple examples, keep going like this x(x-1)(x+1)(x-2)(x+2)... and so on. Proof of the example is easy. Proof of the general: The Fundamental Theorem of Algebra states that a polynomial of the nth degree can have at most n roots. If one derives the factored form of such an equation, it is plain to see, due to the product rule, that one degree drops off. The resulting equation must have n-1 roots. Because the definition of a critical is the root of a derivative, QED B) For n is odd or zero, 0. For n is even and not zero, 1. Best examples are in the form of x^n The proof of the general is simple. An odd function can have 0; a deconstructive proof (Assume a ploynomial of the degree n,… [cont.]
Answered by Turiski - Mon Apr 27 20:57:20 2009
Q. Let f(x) be a polynomial of degree n. a) What is the maximum number of critical points f(x) can have? For each n, give an example with proof of a polynomial having the maximum number for that n. b) Answer the same question with 'maximum' replaced by 'minimum'.
Asked by Ohhhhh heyy - Mon Apr 27 20:37:30 2009 - - 4 Answers - 0 Comments
A. A) n-1. Example is x^3-x, it has two. If you need multiple examples, keep going like this x(x-1)(x+1)(x-2)(x+2)... and so on. Proof of the example is easy. Proof of the general: The Fundamental Theorem of Algebra states that a polynomial of the nth degree can have at most n roots. If one derives the factored form of such an equation, it is plain to see, due to the product rule, that one degree drops off. The resulting equation must have n-1 roots. Because the definition of a critical is the root of a derivative, QED B) For n is odd or zero, 0. For n is even and not zero, 1. Best examples are in the form of x^n The proof of the general is simple. An odd function can have 0; a deconstructive proof (Assume a ploynomial of the degree n,… [cont.]
Answered by Turiski - Mon Apr 27 20:57:20 2009
How do i write a polynomial function of least degree that has real coeficents, the given zeros of the function?
Q. How do i write a polynomial function of least degree that has real coeficents, the given zeros of the function? Given Zeros: 2, -2, 3
Asked by Kasie - Wed Jun 3 18:40:15 2009 - - 1 Answers - 0 Comments
A. since those are zeros then you could say (x-2)(x+2)(x-3)=0 then just distribute
Answered by Paulie Walnuts - Wed Jun 3 18:44:45 2009
Q. How do i write a polynomial function of least degree that has real coeficents, the given zeros of the function? Given Zeros: 2, -2, 3
Asked by Kasie - Wed Jun 3 18:40:15 2009 - - 1 Answers - 0 Comments
A. since those are zeros then you could say (x-2)(x+2)(x-3)=0 then just distribute
Answered by Paulie Walnuts - Wed Jun 3 18:44:45 2009
How do I write a polynomial function with rational coeffcients in standard form, with the given zeros?
Q. I need to write a polynomial function with rational coefficents in standard form. with the zeros 2i, and suare root of 3 I need the full function.
Asked by joeblake15 - Sun Jan 6 02:05:05 2008 - - 4 Answers - 0 Comments
A. f(x) = (x - 2i)(x + 2i)(x + 3)(x - 3) = (x - 4i )(x - 3) = (x + 4)(x - 3) = x^4 - 3 x + 4 x - 12 = x^4 + x -12 => f(x) = x^4 + x -12
Answered by piano - Sun Jan 6 02:25:06 2008
Q. I need to write a polynomial function with rational coefficents in standard form. with the zeros 2i, and suare root of 3 I need the full function.
Asked by joeblake15 - Sun Jan 6 02:05:05 2008 - - 4 Answers - 0 Comments
A. f(x) = (x - 2i)(x + 2i)(x + 3)(x - 3) = (x - 4i )(x - 3) = (x + 4)(x - 3) = x^4 - 3 x + 4 x - 12 = x^4 + x -12 => f(x) = x^4 + x -12
Answered by piano - Sun Jan 6 02:25:06 2008
How do you determine if a polynomial is the difference of two squares?
Q. the answer needs to be in 50 words. i understand what a polynomial is but what i'm getting stuck on is what kind of answer they are looking for, for i have like three answers down, could anyone answer this so i can compare notes and understand this assignment.
Asked by Quinnzel - Sat Aug 8 16:02:43 2009 - - 1 Answers - 0 Comments
A. You determine if a polynomial is the difference of two squares by saying that: The numbers is(are) perfect number(s). The exponent(s) is(are) even. If the numbers are not perfect square, and/or the exponent(s) is(are) not even, then a polynomial is not the difference of two squares. Formula: a -b = (a-b)(a+b) Ex. x -4 = (x-2)(x+2)
Answered by |
Q. the answer needs to be in 50 words. i understand what a polynomial is but what i'm getting stuck on is what kind of answer they are looking for, for i have like three answers down, could anyone answer this so i can compare notes and understand this assignment.
Asked by Quinnzel - Sat Aug 8 16:02:43 2009 - - 1 Answers - 0 Comments
A. You determine if a polynomial is the difference of two squares by saying that: The numbers is(are) perfect number(s). The exponent(s) is(are) even. If the numbers are not perfect square, and/or the exponent(s) is(are) not even, then a polynomial is not the difference of two squares. Formula: a -b = (a-b)(a+b) Ex. x -4 = (x-2)(x+2)
Answered by |
Is a binomial a factor of a polynomial if it leaves a remainder when divided?
Q. Is a binomial a factor of a polynomial if it leaves a remainder when divided? Thanks! you saved my ass, your Mcawesome!
Asked by Superbung - Tue Dec 23 13:35:50 2008 - - 6 Answers - 0 Comments
A. In many books, this is called "The remainder Theorem"... it goes like this: If a polynomial p(x) is divided by (x-r) then the remainder will be p(r). Since you claim that "there is a remainder" you really mean that the remainder is non-zero. Having p(r) not equal to zero means that p(x) cannot be rewriten as (x-r)q(x) for any polynomial q.
Answered by Mike Robertson - Tue Dec 23 13:46:05 2008
Q. Is a binomial a factor of a polynomial if it leaves a remainder when divided? Thanks! you saved my ass, your Mcawesome!
Asked by Superbung - Tue Dec 23 13:35:50 2008 - - 6 Answers - 0 Comments
A. In many books, this is called "The remainder Theorem"... it goes like this: If a polynomial p(x) is divided by (x-r) then the remainder will be p(r). Since you claim that "there is a remainder" you really mean that the remainder is non-zero. Having p(r) not equal to zero means that p(x) cannot be rewriten as (x-r)q(x) for any polynomial q.
Answered by Mike Robertson - Tue Dec 23 13:46:05 2008
How do I determine whether or not a polynomial is a perfect square trinomial?
Q. How do I determine whether or not a polynomial is a perfect square trinomial?
Asked by purpuhlrowboht - Mon Nov 16 20:00:41 2009 - - 1 Answers - 0 Comments
Q. How do I determine whether or not a polynomial is a perfect square trinomial?
Asked by purpuhlrowboht - Mon Nov 16 20:00:41 2009 - - 1 Answers - 0 Comments
What is the best algorithm for solving polynomial roots?
Q. I have been looking at several algorithms for solving roots of polynomial and some of them are quite reasonable. But which is the best algorithm? I would like to find one that is: easy to write in program language, can solve complex roots unlike the bisection method, and convergence is fast and almost guaranteed. Thanks
Asked by John221 - Mon Dec 22 21:40:43 2008 - - 3 Answers - 0 Comments
A. Are there any conditions on the polynomials? Particularly: 1. the nature of the coefficients 2. the degree? In any case try the wikipedia link below. If you have been tinkering, you've probably already seen it, but just in case you haven't, it contains numerous links. You might also try reverse engineering some of the freeware graphers out there... Keep us posted on your results. bye for now. --ADDED-- Newton's method (previous post) does not meet the criteria you have cited of fast and guaranteed convergence. --Adding again-- A link to a bound theorem for real roots (related to Sturm's) that may be helpful for initial values if using Newton.
Answered by Toddio - Mon Dec 22 22:00:17 2008
Q. I have been looking at several algorithms for solving roots of polynomial and some of them are quite reasonable. But which is the best algorithm? I would like to find one that is: easy to write in program language, can solve complex roots unlike the bisection method, and convergence is fast and almost guaranteed. Thanks
Asked by John221 - Mon Dec 22 21:40:43 2008 - - 3 Answers - 0 Comments
A. Are there any conditions on the polynomials? Particularly: 1. the nature of the coefficients 2. the degree? In any case try the wikipedia link below. If you have been tinkering, you've probably already seen it, but just in case you haven't, it contains numerous links. You might also try reverse engineering some of the freeware graphers out there... Keep us posted on your results. bye for now. --ADDED-- Newton's method (previous post) does not meet the criteria you have cited of fast and guaranteed convergence. --Adding again-- A link to a bound theorem for real roots (related to Sturm's) that may be helpful for initial values if using Newton.
Answered by Toddio - Mon Dec 22 22:00:17 2008
How do I determine symmetry of a polynomial function?
Q. How could I determine whether a polynomial function would be symmetric about the y-axis, x-axis, or origin? Consider x^8-x?
Asked by The know-nothing. - Tue Apr 7 03:38:23 2009 - - 2 Answers - 0 Comments
A. First of all, symmetric about the x-axis doesn't make sense. If something was symmetric about the x-axis, then it wouldn't even be a function. It will fail the vertical line test. symmetric about the y-axis implies f(x)=f(-x) and symmetric around the origin implies f(-x)=-f(x). Your function is neither.
Answered by The Prince - Tue Apr 7 03:45:59 2009
Q. How could I determine whether a polynomial function would be symmetric about the y-axis, x-axis, or origin? Consider x^8-x?
Asked by The know-nothing. - Tue Apr 7 03:38:23 2009 - - 2 Answers - 0 Comments
A. First of all, symmetric about the x-axis doesn't make sense. If something was symmetric about the x-axis, then it wouldn't even be a function. It will fail the vertical line test. symmetric about the y-axis implies f(x)=f(-x) and symmetric around the origin implies f(-x)=-f(x). Your function is neither.
Answered by The Prince - Tue Apr 7 03:45:59 2009
How do you find out if a expression is a polynomial?
Q. How do you find out if a expression is a polynomial? What is a polynomial? Thank you.
Asked by Nichole[never gives up] - Sat May 10 12:56:40 2008 - - 3 Answers - 0 Comments
A. a polynomial has more than one term the terms in a polynomial are separated by addition or subtraction
Answered by Rima - Sat May 10 13:12:09 2008
Q. How do you find out if a expression is a polynomial? What is a polynomial? Thank you.
Asked by Nichole[never gives up] - Sat May 10 12:56:40 2008 - - 3 Answers - 0 Comments
A. a polynomial has more than one term the terms in a polynomial are separated by addition or subtraction
Answered by Rima - Sat May 10 13:12:09 2008
How to solve for an extra variable in a polynomial to the third degree? Any geniuses?
Q. At the moment, I'm having some trouble with a polynomial to the third degree. If (x-2) is a factor of x^3 - 7x^2+kx-12, then k = Given a factor, (x-2), I'm assuming one of the values of x = 2; however, I haven't a clue how to solve for k.
Asked by G L C. - Sun Jun 21 14:03:24 2009 - - 5 Answers - 0 Comments
A. if (x-2) is a factor then the equation will be equal to 0 when x=2. substitute 2 in x and equate the equation to 0. so 2^3 - 7x2^2 +kx2 -12 = 0 8-28-12 +2k =0 -32 +2k = 0 2k= 32 k= 16
Answered by i m bored!! - Sun Jun 21 14:27:43 2009
Q. At the moment, I'm having some trouble with a polynomial to the third degree. If (x-2) is a factor of x^3 - 7x^2+kx-12, then k = Given a factor, (x-2), I'm assuming one of the values of x = 2; however, I haven't a clue how to solve for k.
Asked by G L C. - Sun Jun 21 14:03:24 2009 - - 5 Answers - 0 Comments
A. if (x-2) is a factor then the equation will be equal to 0 when x=2. substitute 2 in x and equate the equation to 0. so 2^3 - 7x2^2 +kx2 -12 = 0 8-28-12 +2k =0 -32 +2k = 0 2k= 32 k= 16
Answered by i m bored!! - Sun Jun 21 14:27:43 2009
How do you show that over every finite field, there is an irreducible polynomial of degree 2?
Q. How do you show that over every finite field, there is an irreducible polynomial of degree 2? I know there is a theorem stating that we can find an irreducible polynomial of every degree in a finite field, but how do you prove this specific case?
Asked by Alex - Thu Feb 5 17:17:28 2009 - - 1 Answers - 0 Comments
A. When the characteristic of F is not 2, it's enough to show that not every element is a square. (When the characteristic is 2, every element is a square, so we've got to try something else.) The multiplicative group F* is always cyclic, and if F has odd characteristic, then F has an odd number of elements, so F* has even order. So if F* =, then g^(2k+1) doesn't have a square root in F for any integer k, and so x^2-g^(2k+1) is irreducible. If F has characteristic 2, we have to be a little more careful. Consider the map: F -> F, x |-> x^2+x This is a homomorphism of additive groups. Indeed, we have for all x, y in F: (x+y)^2+x+y = x^2+2xy+y^2+x+y = (x^2+x)+(y^2+y) Now the kernel of this homomorphism is nontrivial, since 1^2+1 =… [cont.]
Answered by John B - Fri Feb 6 14:27:15 2009
Q. How do you show that over every finite field, there is an irreducible polynomial of degree 2? I know there is a theorem stating that we can find an irreducible polynomial of every degree in a finite field, but how do you prove this specific case?
Asked by Alex - Thu Feb 5 17:17:28 2009 - - 1 Answers - 0 Comments
A. When the characteristic of F is not 2, it's enough to show that not every element is a square. (When the characteristic is 2, every element is a square, so we've got to try something else.) The multiplicative group F* is always cyclic, and if F has odd characteristic, then F has an odd number of elements, so F* has even order. So if F* =
Answered by John B - Fri Feb 6 14:27:15 2009
Is there a online Calculator that can solve higer degree polynomial equations for free?
Q. And they can find the zeros of the polynomial and factor them into first degrees.
Asked by Nicholas - Fri Apr 24 17:23:10 2009 - - 2 Answers - 0 Comments
A. You can download a free quadratic solver here: You can download a free polynomial solver here: These solvers can solve your math problems step-by-step
Answered by Sakagami Tomoyo - Mon Apr 27 14:32:05 2009
Q. And they can find the zeros of the polynomial and factor them into first degrees.
Asked by Nicholas - Fri Apr 24 17:23:10 2009 - - 2 Answers - 0 Comments
A. You can download a free quadratic solver here: You can download a free polynomial solver here: These solvers can solve your math problems step-by-step
Answered by Sakagami Tomoyo - Mon Apr 27 14:32:05 2009
From Yahoo Answer Search: 'polynomial'
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PhysOrg.com
A mathematical expression that involves N's and N 2 s and N's raised to other powers is called a polynomial , and that's what the P in P = NP stands for. ...
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dept.physics.upenn.edu
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quadcube gif 12 Nov 1999 16 04 1 2K quadratic polynomial curves gif 12 Nov 1999 15 50 2 8K quadratic polynomial curves mini gif 12 Nov 1999 15 57 2 6K quadrupole gif 22 Oct 2002 17 14 12K
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Alan Zeichick
Wed, 14 Oct 2009 17:51:01 GM
I clearly remember studying the classes of problems deemed NP non-. polynomial. time as I think of it, but more properly defined as nondeterministic . polynomial. time. However, that was a long time ago. ...
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