# Thread: Finding Zeros of a Polynomial

1. ## Finding Zeros of a Polynomial

Hello, all.

I need to find the zeros of the following polynomial so that I can graph it:

$f(x)=3x^2-x^4-2x$

First I factored out x and got:

$x(-x^3+3x-2)$

I used synthetic division to find another zero (-2) and so I now have:

$x(x+2)(-x^2+2x-1)$

I'm not sure how I can go any further. Can $-x^2+2x-1$ be factored out?

Thanks!

2. Originally Posted by JennyFlowers
Hello, all.

I need to find the zeros of the following polynomial so that I can graph it:

$f(x)=3x^2-x^4-2x$

First I factored out x and got:

$x(-x^3+3x-2)$

I used synthetic division to find another zero (-2) and so I now have:

$x(x+2)(-x^2+2x-1)$

I'm not sure how I can go any further. Can $-x^2+2x-1$ be factored out?

Thanks!
$-(x^2-2x+1) = -(x-1)^2$