How do you factor completely 3a^2+9a-12?

1 Answer
Apr 11, 2016

3(a-1)(a+4)

Explanation:

3 is the factor common to all the terms.
Let's take it out

3(a^2+3a-4)

Now, we find the factors of (a^2+3a-4)

Use splitting of the middle term to find the answer.

Find a pair of factors of 1xx-4=-4 which sum up to 3. The pair -1 and 4 works.

Write the expression, (a^2+3a-4) as:

a^2-a+4a-4

Take out the common terms

a(a-1)+4(a-1)

Separate the like terms and you get

(a-1)(a+4)

The factors of 3a^2+9a-12 = 3(a-1)(a+4)