How is dividing a polynomial by a binomial similar to or different from the 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 Dedicated - Tue Nov 10 16:36:41 2009 - - 1 Answers - 0 Comments

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

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

How do the degree of a polynomial relate to the number of zeros?
Q. How do the degree of a polynomial relate to the number of zeros?
Asked by bub - Tue Dec 16 20:35:29 2008 - - 4 Answers - 0 Comments

A. If you are considering both real and complex solutions, then the number of solutions equals the degree of the polynomial (Fundamental Theorem of Algebra). If the solutions can only be real numbers, then the number of solutions is less than or equal to the degree of the polynomial. Example: x^2-4 has degree 2 and the 2 real solutions 2 and -2 x^2+4 has degree 2, but 0 real solutions. Taking into account the complex solutions 2i and -2i, then the degree and the number of solutions is again equal.
Answered by MathPhD - Wed Dec 17 18:19:42 2008

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

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

What number must you add to the polynomial below to complete the square?
Q. alright on the last one i was getting questions, then I just divided it by two then squared it, which is what i needed to know, but that doesn't seem to be working now. What number must you add to the polynomial below to complete the square? x2 - 9x that would be 4.5*4.5 which is 20.25 ?
Asked by Carl W - Mon Mar 30 10:32:54 2009 - - 3 Answers - 0 Comments

A. x^2-9x (-9/2)^2=81/4 so x^2-9x+81/4=(x-9/2)^2 answer//
Answered by Engr. Ronald - Mon Mar 30 10:42:10 2009

What is the complete polynomial with these certain zeroes?
Q. Okay, so they actually give you the zeroes in this problem. It says, not exactly: The zeroes of a given polynomial of the 4th degree are 3 and (3-i). The 3 has a multiplicity of 2. What polynomial has the zeroes of those stated above?
Asked by ecstasyorlove - Thu Mar 22 23:17:04 2007 - - 3 Answers - 0 Comments

A. The FOIL part is actually quite messy. I'd suggest noting the following : (x + a + bi)(x + a - bi) = x^2 + 2ax + (a^2 + b^2) For your problem, a = -3 and b = 1. Therefore, the quadratic part with the imaginary roots is x^2 - 6x + 10. Combine that with the quadratic with the real roots, and you get: (x^2 - 6x + 10)(x^2 - 6x + 9) If my math is right, that expands to: x^4 - 12x^3 + 55x^2 - 114x + 90 OK, let's check with x = 3. The positive terms come to 81 + 495 + 90 = 666. The negative terms come to -324 + -342 = -666. OK, the math checks, but these two 666 really creep me out...
Answered by zanti3 - Thu Mar 22 23:39:14 2007

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

What kind of data is best described by a polynomial regression model?
Q. In other words: What kind of data does a polynomial model describe. How will I know if a poynomial regression model is the best model to use for my data?
Asked by Matt C - Sun Feb 22 20:24:44 2009 - - 1 Answers - 0 Comments

A. When trying to discover a relationship between two variables based on observational information, the first step after data collection is viewing a visual relationship of the data. Many textbook examples will be setups; the data will appear clearly linear, or clearly independent. However, in real-life situations, you have to base your model on what the data looks like TO YOU. Does the data appear to generally tend towards a parabola, or maybe a third or fourth degree curve? For higher degree estimates, you are essentially asking how many times the data trend seems to change directions. It's an "eyeball estimate", really. A polynomial model can describe any particular relationship, if the data curve tends closely enough to that pattern. … [cont.]
Answered by Milo - Wed Feb 25 12:50:29 2009

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

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

How can I make this polynomial function?
Q. I need a polynomial with a degree of five and has four distinct zeros. How does this look, or, at least, what are the zeros?
Asked by avery g - Thu Jan 8 21:48:53 2009 - - 1 Answers - 0 Comments

A. if it could be any polynomial just work backwards and construct one from factors IE (x+1)(x+2)(x+3)(x+4)^2 NOTE: since you need degree 5 but has only 4 roots one of the terms will require a square now all you have to do is foil out these and you will have a polynomial degree 5 with 4 roots (one will be a repeated root.) edit: to make it easier on the brain choose x^2(x+1)(x+2)(x+3) this yields zeros of 0,-1,-2,-3 and still gets you a degree 5 polynomial edit of edit: this gets you x^5+6x^4+11x^3+6x^2 this will factor to x^2(x+1)(x+2)(x+3)
Answered by Aaron - Thu Jan 8 21:59:04 2009

What polynomial represents the new area?
Q. Joseph's basketball court is square, with one side being "x" feet. He decides to lengthen one side by 8 feet, and shorten the other side by 2 feet. What polynomial represents the new area?
Asked by bigsexy_velvet - Mon Nov 3 17:46:47 2008 - - 1 Answers - 0 Comments

A. (x + 8)(x-2) = x^2 + 6x - 16
Answered by Coolio - Mon Nov 3 17:50:32 2008

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

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

How do you find a polynomial by its zeros?
Q. If a polynomial has only two zeros, its degree is going to be 2 right? and also, how do you find a polynomial by its zeros? Also, how do you find two polynomials that share the same two zeros?
Asked by scdesperado15 - Sat Jun 6 16:05:29 2009 - - 4 Answers - 0 Comments

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

How to write a polynomial function in standard form?
Q. Need help writing a polynomial function in standard form with real coefficients whose zeros and their multiplicities include those listed. -1 (Multiplicity 2), -2 - i (multiplicity 1)
Asked by Kevin - Mon Sep 28 02:18:25 2009 - - 1 Answers - 0 Comments

A. -1 (Multiplicity 2) x = -1 x + 1 = 0 === (x+1)^2 = 0 === x = -2 - i imaginary roots occur with conjugate [- 2 + i] is also zero === [x + 2 + i][x + 2 - i] = 0 === combine (x+1)^2 [x + 2 + i][x + 2 - i] = 0 (x+1)^2 [(x + 2)^2 + 1] = 0 f(x) = polynomial = (x^2+2x+1) [x^2 + 4x + 5] f(x) = (x^2+2x+1) [x^2 + 4x + 5] multiply and but in form f(x) = ax^4 + bx^3 + cx^2 + dx + e
Answered by anil bakshi - Wed Sep 30 02:15:27 2009

How do i arrange a polynomial with powers of x in descending order?
Q. **In the problem below, the number in the "()" is an exponent** Arrange the terms of the polynomial 4+3x(3)y(3)-x(5)y_xy so that the powers of x are in descending order. please dont answer if you dont know the answer to that question. this question goes out to more of the algebra teachers. i need this answer ASAP. thanks.
Asked by Nikki! - Mon Mar 23 22:08:49 2009 - - 1 Answers - 0 Comments

A. 4+(3x^3)(y^3)-(x^5)y-xy Start with first term that has the highest Power on x value, then next term with Less power on x and so on.. In your example, this would be: -(x^5)y + (3x^3)(y^3) - xy + 4
Answered by AMMAR e T - Mon Mar 23 22:56:21 2009