Question

list the possible rational zeros of f(x)=x^5-2x^4+8x^2-13x+6.

Then factor this polynomial completely over the set of complex numbers

Answer 1

Do you know about the rational root theorem?

Answer 2

kinda

Answer 3

Well, you can use that to find the possible rational zeros. The leading coefficient of the polynomial is 1, so the positive and negative factors of the trailing coefficient will be the potential factors. What are the factors of 6?

Answer 4

+/-1, +/-2,+/-3,+/-6

Answer 5

Right. So those are the possible rational zeros.

Now the tedious part: try each of them out and see which are true zeros (\f(x) = 0\) when you plug them in). When you find a value \(r_n\) that is a zero of the polynomial \(f(x)\), divide the polynomial by \(x-r_n\) and repeat the process. That will get out all of the rational roots, and any polynomial that remains will have only complex roots.

Answer 6

ok