Question

I am not totally understanding this process.

Factor Completely:

x^5y^2 - x^4y^2 - 2x^3y^2

Answer 1

Complete factoring is the process of breaking the expression down into a multiplicative product of terms that can't be broken down any further. Here, you can simplify the expression you're given quite a bit just by noting that all three terms in it are divisible by both x^3 and y^2, so there are two of your factors already. The whole expression can therefore be expressed as:

(x^3) times (y^2) times (x^2 - x - 2)

Can we do any better than that? Actually yes: that last bracket can be factored into

(x+1) times (x-2)

How did I know that? If I can express (x^2 - x - 2) as the product of two brackets which look like (x+a) times (x+b) for some a and b, then (a times b) must be -2, and (a plus b) must be -1. If a = 1 and b = -2, I'll get the right answer, so I've found a solution that works. I can't see any more simplification I can do, so the final answer should be x^3 times y^2 times (x+1) times (x-2).

Answer 2

Thanks!