How can I factor: a + bx + cx^2 + dx^3 + ex^4 + fx^5?

Question

I'm aware that Abel proved that there is no formula to factor polynomials of degree 5 and higher, but I understand that you can represent these equations as matrices, and then the eigenvalues are the roots of the equation. How can I construct the matrix for the formula expressed above so that I can find its roots by finding the eigenvalues?

Synthetic division does not help to solve this problem. Also, factoring does not need to be stated in the form of an equation, but if it helps others explain. Solve for the values of x (there are 5 of them) given that the equation above = 0.

Answer 1

You need to know what this is equivalent to in order to form a eigenvalue problem. And this is far different from finding the arbitrary roots to the quintic. Check link for quick primer.

Answer 2

we are able to work out that a is a elementary component on the 1st 2 words, and b is a elementary component in the different 2 words. Now, divide the 1st 2 words by a, and positioned the a outdoors in parentheses. ax / a = x -ay / a = -y, so a(x - y) - bx + by Now, the different 2 words have opposite signs and warning signs. adverse-advantageous words warrant taking the sign of our first term. We divide the two words by -b. -bx / -b = x by / -b = -y, so we get our very final answer: a(x -y) - b(x - y)

Answer 3

sure there are ways to factor polynomials of degree 5 and higher, look up synthetic division.

Answer 4

you cant factor that because you dont have an end solution...what does this equation equal? or...you could figure it out if you knew the value of x.

right now it is an incomplete equation and doesnt value anything

Answer 5

First, get your degrees straight. Put fx^5 first, then ex^4...

4-d matrices? I don't know anything...