Factoring Examples

Find the quotient: .

Yikes, that looks ugly. This problem is a sneaky one, because we need to apply two layers of factoring. Maybe there's a draft.

First, we can pull out a common factor of 2x:

Canceling that factor of 2x from the numerator and denominator gives us:

Then the numerator factors again, so we can rewrite the expression as:

This simplifies to:

4x + 1

All that junk reduces to 4x + 1. Isn't math the most wonderful thing in the world? Smile and nod.

Find the quotient: .

There's more stuff going on there than in a Salvador Dali painting. We'll turn this thing into a calmer, more peaceful Monet if we can. Shall we?

We can factor the numerator by grouping to find this crowded mess:

Then we cancel (y + 3) from the numerator and denominator and get:

xy + 12

Ah. We're reminded of lily pads and haystacks.