Step by step
The question
Question: factor x² + x − 12.
Factor means: write it as a times, with brackets.
x2 + x − 12
1 Find two numbers
We need two numbers.
They multiply to −12, and they add to 1.
? × ? = −12
? + ? = 1
They multiply to a minus number, so one number is plus and one is minus.
They add to a plus number, so the bigger one is plus.
× is − → one +, one −; bigger one +
We list the pairs that make 12, smallest first.
We take the smaller from the bigger.
We need 1.
3 and 4 give 1.
Yes!
With the signs: −3 and 4.
1 × 12: 12 − 1 = 11
2 × 6: 6 − 2 = 4
3 × 4: 4 − 3 = 1 ✓
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 + x − 12
We get x² + x − 12 again.
So (x − 3)(x + 4) is right!
Let's look back.
First: find two numbers.
Last: check.
Answer
= (x − 3)(x + 4)