# polynomial

1. ### Polynomial Division Problem

Polynomial Division Problem Calculate the following and state the remainder: 2x^3+x^2-22x+20 divided by 2x-3 Thanks!
2. ### Polynomial factorization calculator and root finder

Hello folks. I have written a Web calculator that can factor polynomials and it can also find exact roots using rational numbers and radical expressions. You can enter any polynomial expression in the input box. You can see it at: http://www.alpertron.com.ar/POLFACT.HTM Currently, it can...
3. ### Cubic Polynomial Factorizing

How is this equation in the attachment factorized? I need steps, please. Thank you in advance.

Find the quadratic equation which satisfies the condition x_1 x_2 =x_1 +x_2.
5. ### What is this question asking for? Polynomial

Question: Find S as a polynomial in x where S=(x-1)^4+4(x-1)^3+6(x-1)^2+4(x-1)+1 Understanding what is being asked here would be a useful first step:giggle: Do I need to expand the brackets or what? I understand a polynomial to be an expression involving sums of powers of a...
6. ### Some sort of extension to the polynomial remainder theorem?

Two questions on another board I'd like to learn how to solve. 1) $p(x) \equiv 1 \pmod{x+1},~p(x) \equiv -7 \pmod{x+5}$ What is $p(x) \pmod{(x+1)(x+5)}$ ? 2) $x^{1000} \pmod{(x^2+1)(x+1)} = ?$
7. ### Factor polynomial

Hello, When making some exercices to improve my general understanding of basic mathematics, I stumbled upon following problem: to factorise X^2 + ((sqrt 2)+(sqrt 3)) x + (sqrt 6) I do not recognise the form (a+b)^2, so I tried going for the discriminant, which would be ((sqrt 2)+(sqrt...
8. ### Finding the roots of a 6-degree polynomial

Hello, I am having trouble finding the roots of a 6-degree polynomial equation in expression form. I hope anyone can help reduce it to a form where the expression for each root can be determine. Thanks, ZeroKool

Not sure where to start.
10. ### Finding polynomial of a given degree with given zeros: complext zeros

I am stuck on this topic in pre-calculas class. I have practiced and read, watched videos and still stuck. Find polynomial f(x) of degree 4 with real coefficients and the follosing zeros -1,2,-3+i Thanks
11. ### Question about proving the availability of double real root of a polynomial

For part b, it is assuming that n is an odd number, so r-a = r+a Since the exponent of n-1 would be an even number for n being an odd number, is the equation of (r-a)^(n-1) = -(r+a)^(n-1) undefined? It is because any real number to a power of an even number cannot be negative. Please...
12. ### Polynomial Factoring Question

I am consistently getting answers that my book says are wrong, but only in terms of positive or negative signs, with every other thing composing my answer (parenthesis, exponents, coefficients and variables) being consistently correct. The following would be the best representation of what I...
13. ### Polynomial solutions

I'm not able to define the solutions. How many solutions does the polynomial equation below have for n natural? Note: (without complex solutions). \sum_{j=1}^{j=n} x^j =x^n+x^{n-1}+...+x^2+x=0
14. ### Cubic polynomial confusion

Hello. I'm trying to find the fundamental matrix for a differential equation and I am getting completely stuck on this cubic polynomial. $(3-r)[(3-r)(-1-r)+3] -[(-1-r)+3] - [3-3(3-r)] = 0$ (this came from |A-rI| = 0) $\rightarrow -3(3-r) -3r(3-r)+r(3-r)+r^2(3-r) + 14 - 2r = 0$...
15. ### Matrices which satisfy the equation

Show that there are no real 3x3 matrices which satisfy the equation (picture below), but there are complex 3x3 matrices and real 2x2 matrices which satisfy that. I know that this equation has no real roots, but I don't know how to apply that to matrices.
16. ### Irreducible or reducible polynomial?

Hi all, I have used rational root test and obtain this result for the question: f(x) = 2x^4+8x^3+5x^2âˆ’7xâˆ’3=(2x^2+2xâˆ’3)(x^2+3x+1) This shows that there is no linear factor but a quadratic factors instead. Do I still consider such polynomial as reducible or irreducible? Am I...
17. ### polynomial

I would like to have verification if the following attached proof is correct. If it is not correct, what can be done to make it correct? Thanks.
18. ### Sign changes in computing Quartic function

Ferrari method uses simpler cubic equation. For complex coefficients: (0.75, 1.25)x^4 + (1, 0)x^3 + (-1.25, 0)x^2 + (1.5, -0.25)x + (1.75, -1) p=(-0.358131487889273, 0.891003460207612), q=(0.203643395074293, -1.232139222471), r=(0.16504232468481, -1.24136744052394) cubic: (1, 0)z^3 +...