Step by step
The question
Question: factor x² + 7x + 12.
Factor means: write it as a times, with brackets.
x2 + 7x + 12
1 Find two numbers
We need two numbers.
They multiply to 12, and they add to 7.
? × ? = 12
? + ? = 7
They multiply to a plus number, so the two numbers have the same sign.
They add to a plus number, so both are plus.
× is + → same signs: both +
We list the pairs that make 12, smallest first.
We add each pair.
We need 7.
3 and 4 give 7.
Yes!
1 × 12: 1 + 12 = 13
2 × 6: 2 + 6 = 8
3 × 4: 3 + 4 = 7 ✓
The two numbers go in the brackets.
So we get (x + 3)(x + 4).
= (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.
Check: (x + 3)(x + 4) = x2 + 4x + 3x + 12
= x2 + 7x + 12
We get x² + 7x + 12 again.
So (x + 3)(x + 4) is right!
Let's look back.
First: find two numbers.
Last: check.
Answer
= (x + 3)(x + 4)