Step by step
The question
Question: factor x² + 5x + 6.
Factor means: write it as a times, with brackets.
x2 + 5x + 6
1 Find two numbers
We need two numbers.
They multiply to 6, and they add to 5.
? × ? = 6
? + ? = 5
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 6, smallest first.
We add each pair.
We need 5.
2 and 3 give 5.
Yes!
1 × 6: 1 + 6 = 7
2 × 3: 2 + 3 = 5 ✓
The two numbers go in the brackets.
So we get (x + 2)(x + 3).
= (x + 2)(x + 3)
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 + 3) = x2 + 3x + 2x + 6
= x2 + 5x + 6
We get x² + 5x + 6 again.
So (x + 2)(x + 3) is right!
Let's look back.
First: find two numbers.
Last: check.
Answer
= (x + 2)(x + 3)