Solved

# Factoring polynomials with five terms...

Posted on 2007-04-05

Ok, going to try this again... I'd posted a similar Q once but figured it out (maybe I'll be lucky and figure this one out after posting)... anyway...

First off, this is NOT homework, or more specifically it's homework I've assigned myself so I can learn this.

I know how to remove greatest common denominators, and I know how to factor trinomials, and I know how to group to allow factoring...

In this problem:

f(x) = 2x^4 + 14x^3 + 25x^2 - 4x - 28

I know that I can group the first two and the last two and go from here:

2x^3(x + 7) + 25x^2 - 4(x + 7)

to here:

(2x^3 - 4)(x + 7) + 25x^2

But since the stated intent of this problem is "State all possible rational zeros" and I assume that means values for x such that the end result IS zero, I'm stumped as to how to get from my last point to THAT point...

All the things I've found about "grouping" are based on grouping 2 things together.

Understand, I'm interested in knowing HOW to do this, not the answer to this one specifically...

Thanks.