Step by step
The question
Question: factor 8x² − 12x.
Factor means: write it as a times, with brackets.
8x2 − 12x
1 Take out the common factor
A term is one part between the + and − signs.
A common factor goes into every term.
What goes into 8 and 12?
We list the numbers that go into each.
Into 8: 1, 2, 4, 8.
Into 12: 1, 2, 3, 4, 6, 12.
4 is the biggest one in both lists.
Every term has at least x.
So the common factor is 4x.
Into 8: 1, 2, 4, 8
Into 12: 1, 2, 3, 4, 6, 12
every term has x
We divide every term by it.
What is left goes in the bracket.
8x2 ÷ 4x = 2x
−12x ÷ 4x = −3
So it is 4x(2x − 3).
= 4x(2x − 3)
2 Check
Let's check: we multiply it back out.
The term in front times each part.
Check: 4x(2x − 3) = 8x2 − 12x
We get 8x² − 12x again.
So 4x(2x − 3) is right!
Let's look back.
First: take out the common factor.
Last: check.
Answer
= 4x(2x − 3)