Step by step
The question
Question: factor x² + 7x + 12.
Factor means: write it as a times, with brackets.
1 Find two numbers
The rule: we need two numbers.
They multiply to the last number, 12.
They add to the middle number, 7.
Look at the sign in front of 12: it is plus.
So the two numbers have the same sign.
Now the sign in front of 7x: it is plus.
So both are plus.
We list the pairs that make 12, smallest first.
For each pair, we check two things: they multiply to 12, and they add to 7.
1 × 12 = 12.
1 + 12 = 13.
Not 7.
2 × 6 = 12.
2 + 6 = 8.
Not 7.
3 × 4 = 12.
3 + 4 = 7.
Both work!
So the two numbers are 3 and 4.
The two numbers go in the brackets.
So we get (x + 3)(x + 4).
2 Check
Let's check: we multiply it back out.
Each part of the first bracket times each part of the second.
We get x² + 7x + 12 again.
So (x + 3)(x + 4) is right!
Let's look back.
First: find two numbers.
Last: check.