Step by step
The question
Question: factor 2x² + 10x + 12.
Factor means: write it as a times, with brackets.
1 Take out the common factor
2, 10 and 12 can all be divided by 2.
So the common factor is 2.
We divide every term by it.
What is left goes in the bracket.
So it is 2(x² + 5x + 6).
2 Find two numbers
We need two numbers.
They multiply to 6, and they add to 5.
They multiply to a plus number, so the two numbers have the same sign.
They add to a plus number, so both are plus.
We list the pairs that make 6, smallest first.
We add each pair.
We need 5.
2 and 3 give 5.
Yes!
The two numbers go in the brackets.
So we get 2(x + 2)(x + 3).
3 Check
Let's check: we multiply it back out.
Each part of the first bracket times each part of the second.
We get 2x² + 10x + 12 again.
So 2(x + 2)(x + 3) is right!
Let's look back.
First: take out the common factor.
Then: find two numbers.
Last: check.