Step by step
The question
Question: factor 3x³ − 12x.
Factor means: write it as a times, with brackets.
3x3 − 12x
1 Take out the common factor
3 and 12 can both be divided by 3.
Every term has at least x.
So the common factor is 3x.
3, 12: all in the 3 times table
every term has x
We divide every term by it.
What is left goes in the bracket.
3x3 ÷ 3x = x2
−12x ÷ 3x = −4
So it is 3x(x² − 4).
= 3x(x2 − 4)
2 Two squares
This is one square take away another square.
x² is x squared.
4 is 2 squared.
A square minus a square is the plus bracket times the minus bracket.
a² − b² = (a + b)(a − b)
x2 = (x)²
4 = 2²
So we get 3x(x + 2)(x − 2).
= 3x(x + 2)(x − 2)
3 Check
Let's check: we multiply it back out.
Each part of the first bracket times each part of the second.
Check: 3x(x + 2)(x − 2)
= 3x(x2 − 2x + 2x − 4) = 3x(x2 − 4)
= 3x3 − 12x
We get 3x³ − 12x again.
So 3x(x + 2)(x − 2) is right!
Let's look back.
First: take out the common factor.
Then: two squares.
Last: check.
Answer
= 3x(x + 2)(x − 2)