Factoring Polynomials

Question

Factor each polynomial completely. Make sure to check for a GCF first.

w⁴-14w²-32

I'm confused on how to work this out using the difference of squares formula, any help would be appreciated. I kinda need a step-by-step explanation to help me understand.

Answer 1

Since the first term is w⁴, we know that the factored form must look like this.

(w² )(w² )

Next we identify the factors of -32 and see which ones add to -14 The options are:

-1,32

1,-32

2,-16 (This is the correct pair, 2+-16 = -14, which is the middle term.

-2,16

4,-8

-4,8

(w²+2)(w²-16) But, this isn't finished. (w²+2) is prime. But, (w²-16) is not prime, this is a difference of squares.

√w²=w

√16=4

So the final answer is (w²+2)(w+4)(w-4)