Step by step
The question
Question: factor completely 3x² − 12.
Completely means: until no part can be factored any more.
1 Common factor first
3 goes into 12: 3 × 4 = 12.
So 3 goes into both.
So the common factor is 3.
We divide every term by it.
What is left goes in the bracket.
So it is 3(x² − 4).
2 Count the terms
The bracket has 2 terms.
With 2 terms we look for two squares: one square take away another.
x² − 4 is one square take away another square.
x times x is x², so x² is x squared.
2 times 2 is 4.
The rule: one bracket with plus, one with minus.
So we get 3(x + 2)(x − 2).
3 Look at each bracket
Brackets like x + 2 have just x and a number.
They can't be factored.
No bracket can be factored any more.
So we are done.
Careful!
Don't forget the common factor 3 in the answer.
4 Check
Let's check: we multiply it back out.
Each part of one bracket times each part of the other.
Then the common factor times every part.
We get 3x² − 12 again.
So it is right!
Let's look back.
First: common factor.
Then: count the terms.
Then: look at each bracket.
Last: check.