Question

Factor each of the following. Remember: It is the reverse of the distributive property and your first step is to find the greatest common factor of all terms.

Answer 1

To factor using the reverse of the distributive property, find what common factor the numbers have and what common factor the variables have.

10.

-8x - 16

8 is a factor of both -8 and 16.
The first term has x, but the second term does not, so there is no common variable. The only common factor is 8, or -8.

Factor out a -8:

-8x - 16 = -8(x + 2)

To see if the factorization is correct, multiply the answer using the distributive property. If you get the original expression, then the factorization is correct.

11.

w^2 - 4w

The first term only has a factor of 1. The second term has a 4. There is no common factor between 1 and 4 except for 1, so there is no number you can factor out. The first term has w^2. The second term has w. Both terms have a common factor of w. We can factor out w from both terms.

w^2 - 4w = w(w - 4)

12.

4s + 10rs

4 and 10 have a common factor of 2.
s and rs have a common factor of s.
2 times s is 2s, so the common factor is 2s.
We now factor out 2s

4s + 10rs = 2s(2 + 5r)