Step by step
The question
Question: factor x² − 2x − 15.
Factor means: write it as a times, with brackets.
x2 − 2x − 15
1 Find two numbers
We need two numbers.
They multiply to −15, and they add to −2.
? × ? = −15
? + ? = −2
They multiply to a minus number, so one number is plus and one is minus.
They add to a minus number, so the bigger one is minus.
× is − → one +, one −; bigger one −
We list the pairs that make 15, smallest first.
We take the smaller from the bigger.
We need 2.
3 and 5 give 2.
Yes!
With the signs: 3 and −5.
1 × 15: 15 − 1 = 14
3 × 5: 5 − 3 = 2 ✓
The two numbers go in the brackets.
So we get (x + 3)(x − 5).
= (x + 3)(x − 5)
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 − 5) = x2 − 5x + 3x − 15
= x2 − 2x − 15
We get x² − 2x − 15 again.
So (x + 3)(x − 5) is right!
Let's look back.
First: find two numbers.
Last: check.
Answer
= (x + 3)(x − 5)