Step by step
The question
Question: factor x² + 2x − 15.
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, −15.
They add to the middle number, 2.
Look at the sign in front of 15: it is minus.
So one number is plus and one is minus.
Now the sign in front of 2x: it is plus.
So the bigger one is plus.
When we add a plus and a minus, the bigger one wins.
We list the pairs that make 15, smallest first.
For each pair, we check two things: they multiply to 15, and the bigger take away the smaller is 2.
One is minus, so adding them is a take away.
1 × 15 = 15.
15 − 1 = 14.
Not 2.
3 × 5 = 15.
5 − 3 = 2.
Both work!
So the two numbers are 3 and 5.
With the signs: −3 and 5.
The two numbers go in the brackets.
So we get (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.
We get x² + 2x − 15 again.
So (x − 3)(x + 5) is right!
Let's look back.
First: find two numbers.
Last: check.