The Reverse Gear

Here is your first factoring. In 3x + 12, both terms are divisible by 3. So you can take the 3 out in front and keep what is left inside parentheses: 3x + 12 = 3(x + 4).

To find what is left, divide each term by the factor you took out: 3x ÷ 3 = x and 12 ÷ 3 = 4. Factoring uses the distributive property in reverse. Instead of multiplying the 3 into the parentheses, you take it out.

Every factoring in this section works the same way. Find a factor that every term shares, take it out in front, and keep what is left inside the parentheses. The hard part is spotting what the terms share. The next chapters practise that on bigger and bigger expressions.