Step by step
The question
Question: factor x² + 3x − 10.
Factor means: write it as a times, with brackets.
x2 + 3x − 10
1 Find two numbers
We need two numbers.
They multiply to −10, and they add to 3.
? × ? = −10
? + ? = 3
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 10, smallest first.
We take the smaller from the bigger.
We need 3.
2 and 5 give 3.
Yes!
With the signs: −2 and 5.
1 × 10: 10 − 1 = 9
2 × 5: 5 − 2 = 3 ✓
The two numbers go in the brackets.
So we get (x − 2)(x + 5).
= (x − 2)(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 − 2)(x + 5) = x2 + 5x − 2x − 10
= x2 + 3x − 10
We get x² + 3x − 10 again.
So (x − 2)(x + 5) is right!
Let's look back.
First: find two numbers.
Last: check.
Answer
= (x − 2)(x + 5)