Factoring another polynomial function

Quote:

Originally Posted by Arise01

Alright so I've started this one as well.

Question: Determine the x - intercepts of the polynomial function.

-36x^4+14x^3+2x^2

I've factored down to ...

2x^2(18x^2+7x+1)

So I'm guessing that I'm going to have to use trial and error. How would I go about using trial and error for future reference?

First you have a slight error when you factored out the GCF

$-2x^2(18x^2-7x-1)$

Now if we multiply a and c together we get

$-18$

Now we need factors of

$-18$

That add up to

$-7 = -9+2$

So we split the middle term to get

$-2x^2[18x^2-9x+2x-1]=-2x^2[9x(2x-1)+(2x-1)]=$

$-2x^2[(2x-1)(9x+1)]$