In polynomial equations, what is the best way to getting the multiples of the two multiplied numbers?
Q. For example, x^2 + 4x-170=0 I know I have to multiply the coefficients of the highest polynomial and the lowest. Which is -170. But when it comes to getting the multiples of -170 what's the easiest way in getting two multiples that result in the middle number 4?
Asked by Symphonic - Mon Dec 1 15:37:35 2008 - - 4 Answers - 0 Comments

A. This can only be done by quadratic formula. x = [-4 +/- sqrt(4^2 - 4*-170)]/2 ...[-4 +/- sqrt(16 + 680)]/2 ...[-4 +/- sqrt(696)]/2 ...[-4 +/- sqrt(4*3*2*29)]/2 ...[-4 +.- 2 sqrt174]/2 ...-2 +/- sqrt 174
Answered by Dee W - Mon Dec 1 15:46:42 2008

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

Find a polynomial with integer coefficients and a leading coefficient of one that satisfies?
Q. Find a polynomial with integer coefficients and a leading coefficient of one that satisfies the given conditions. Q has degree 3, and zeros -5 and 1 + i. Q(x) =?
Asked by Math - Tue Sep 22 16:23:09 2009 - - 1 Answers - 0 Comments

A. x^3+ kx^2 + m*x + c (x+5)(x-(1+i))(x-(1-i)) = (x+5)(x^2-x(1+i)-x(1-i)+( 1-i^2) = x^3 -2x^2 +2x +5x^2 -10x+ 10 = x^3+3x^2-8x+10 k=3, m=-8, c=10 Q(x)=x^3 + 3x^2 - 8x+ 10
Answered by SuperA - Tue Sep 22 16:42:56 2009

How do you find a polynomial with zeros given?
Q. I've been given 2, -3, and 1-2i as the zeros and I need to find a polynomial containing those zeros with real coefficients. How would I do that?
Asked by confused guy - Wed Dec 17 20:31:34 2008 - - 2 Answers - 0 Comments

A. Since 2 is a zero, (x - 2) is a factor Since -3 is a zero, (x + 3) is a factor Since 1 - 2i is a zero, its conjugate 1 + 2i is also a root. Find trinomial with the above complex numbers as roots. Sum of roots = (1 - 2i) + (1 + 2i) = 2 = -b; b = -2 Product = (1 - 2i)(1 + 2i) = 1 + 4 = 5 = c (x^2 - 2x + 5) is a factor polynomial f(x) = (x - 2)(x + 3)(x^2 - 2x + 5) f(x) = (x^2 + x - 6)(x^2 - 2x + 5) f(x) = x^4 - x^3 - 3x^2 + 17x - 30
Answered by Jerome J - Wed Dec 17 20:40:48 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 __A_YAHOO_USER__ - 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 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 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 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

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

How do you find the roots of a polynomial when given a complex root?
Q. I have an ugly homework problem that I want to solve myself--I'm not looking for the answer (yet!), only how to do the problem. The problem is: Find the roots of x^4 - 2x^3 + 14x^2 - 8x + 40 given 2i is a root. I will NOT choose as an answer anyone who just solves this problem and provides the answer. I really need to learn how to do this stuff. So the best answer will be one that helps me learn to do this--preferably with another example similar to the problem. So I know that (x - 2i) and (x + 2i) are factors -- creating (x^2 + 4), but I can't figure out how to divide the polynomial by either 1) a complex number or 2) a 2nd degree polynomial. I understand dividing a polynomial by (x - c) and also synthetic division, just not… [cont.]
Asked by Erika S - Sat Mar 17 22:01:24 2007 - - 5 Answers - 0 Comments

A. Just use long division: __x _-2x_+10___ x +4| x^4-2x +14x -8x+40 x^4 + 4x ___ -2x +10x -8x -2x -8x ___ 10x + 40 10x + 40 ___ As you can see, the other factor is x -2x+10. Setting this to zero and solving gives x = 1/2(2 + 6i) = 1 + 3i and x = 1-3i. Since YA doesn't space properly, I'll be back to show you 2 other ways to do this. One of these is a method of synthetic division for quadratic polynomials Method 2: The problem is: You are factorising a quartic. You know a quadratic factor. How do you find the other factor? Let's use your example: x^4-2x +14x -8x+40= (x +4)(x +px+q) Equate coefficients of like powers of x: Equating the constant terms gives 4q = 40 q = 10. Equating the coefficients of x gives p = -2. [cont.]
Answered by steiner1745 - Sat Mar 17 22:33:21 2007

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

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

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 su u uo p - Sat Aug 8 16:11:56 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 SuperPi - 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

When might it be better to solve a quadratic equation by factoring the polynomial without first?
Q. When might it be better to solve a quadratic equation by factoring the polynomial without first putting it in standard form? Not too sure. Perfect square form? or is that even a form?
Asked by __A_YAHOO_USER__ - Fri Dec 14 22:04:38 2007 - - 1 Answers - 0 Comments

A. I would say that you would generally want to put in in standard form: ax2+bx+ c, first no matter what the situation. It would make factoring easier and defines the constants a,b,&c for the quadratic equation.
Answered by kennyk - Fri Dec 14 22:19:25 2007

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 13:02:09 2008 - - 2 Answers - 0 Comments

A. If you don't want to be bugged for the rest of your mathematical life it is worth while to have a clear concept of polynomials. Wikipedia is good.
Answered by Frank K - Sat May 10 13:14:13 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

A. Suppose f(x) = 0 for x = a and x = b. Then f(x) = (x - a)(x - b) = x - ax - bx + ab Example (zeroes at x = 3 and x = -2) f(x) = x -3x - (-2)x + 3(-2) = x - x - 6
Answered by Marlon JD - Sat Jun 6 16:09:37 2009

How do you find the zeros of these polynomial functions?
Q. Our teacher explained this to us in a hurry as the bell was going to ring and the book doesn't explain it at all. Can someone show me/help me understand how to find the zeros of the following polynomial functions? The problems are: f(x) = -x + 12x - 35 h(x) = -3x + 2x + 5 Any help is greatly appreciated.
Asked by Ashley F - Sun Mar 30 16:16:46 2008 - - 1 Answers - 0 Comments

A. Factor out a -1 first, then factor normally: f(x) = -(x^2 -12x +35) = -1(x-5)(x-7) x=5, x=7 h(x) = - ( 3x^2 -2x -5) = - (3x -5)(x +1) 3x-5 =0, 3x=5, x =5/3 x=1=0, x= -1
Answered by William B - Sun Mar 30 16:24:50 2008

How can we relate polynomial functions to real life situations?
Q. I need to do this project where i am supposed to figure out whats the relation between real life situations and polynomial functions plzz i need the answer asap thnxx alot
Asked by Lele - Sat Feb 27 16:03:37 2010 - - 0 Answers - 0 Comments