Step by step
The question
Question: factor x² − 6x + 8.
Factor means: write it as a times, with brackets.
x2 − 6x + 8
1 Find two numbers
We need two numbers.
They multiply to 8, and they add to −6.
? × ? = 8
? + ? = −6
They multiply to a plus number, so the two numbers have the same sign.
They add to a minus number, so both are minus.
× is + → same signs: both −
We list the pairs that make 8, smallest first.
We add each pair.
We need 6.
2 and 4 give 6.
Yes!
With the signs: −2 and −4.
1 × 8: 1 + 8 = 9
2 × 4: 2 + 4 = 6 ✓
The two numbers go in the brackets.
So we get (x − 2)(x − 4).
= (x − 2)(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 − 2)(x − 4) = x2 − 4x − 2x + 8
= x2 − 6x + 8
We get x² − 6x + 8 again.
So (x − 2)(x − 4) is right!
Let's look back.
First: find two numbers.
Last: check.
Answer
= (x − 2)(x − 4)