The question
Question: factor 6x² + 9x.
Factor means: write it as a times, with brackets.
6x2 + 9x
1 Take out the common factor
6 and 9 can both be divided by 3.
Every term has at least x.
So the common factor is 3x.
6, 9: all in the 3 times table
every term has x
We divide every term by it.
What is left goes in the bracket.
6x2 ÷ 3x = 2x
9x ÷ 3x = 3
So it is 3x(2x + 3).
= 3x(2x + 3)
2 Check
Let's check: we multiply it back out.
The term in front times each part.
Check: 3x(2x + 3) = 6x2 + 9x
We get 6x² + 9x again.
So 3x(2x + 3) is right!
Let's look back.
First: take out the common factor.
Last: check.
▶ Watch it solved
The question
Question: factor x² + x − 12.
Factor means: write it as a times, with brackets.
x2 + x − 12
1 Find two numbers
We need two numbers.
They multiply to −12, and they add to 1.
? × ? = −12
? + ? = 1
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 12, smallest first.
We take the smaller from the bigger.
We need 1.
3 and 4 give 1.
Yes!
With the signs: −3 and 4.
1 × 12: 12 − 1 = 11
2 × 6: 6 − 2 = 4
3 × 4: 4 − 3 = 1 ✓
The two numbers go in the brackets.
So we get (x − 3)(x + 4).
= (x − 3)(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 − 3)(x + 4) = x2 + 4x − 3x − 12
= x2 + x − 12
We get x² + x − 12 again.
So (x − 3)(x + 4) is right!
Let's look back.
First: find two numbers.
Last: check.
▶ Watch it solved
The question
Question: factor 6x² + 7x − 3.
Factor means: write it as a times, with brackets.
6x2 + 7x − 3
1 Find two numbers
The number in front of x² is 6.
So we multiply 6 by −3: that is −18.
We need two numbers that multiply to −18 and add to 7.
6 × (−3) = −18
? × ? = −18, ? + ? = 7
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 18, smallest first.
We take the smaller from the bigger.
We need 7.
2 and 9 give 7.
Yes!
With the signs: −2 and 9.
1 × 18: 18 − 1 = 17
2 × 9: 9 − 2 = 7 ✓
2 Split the middle
We write 7x as −2x + 9x.
It is the same amount.
= 6x2 − 2x + 9x − 3
3 Group in pairs
We put the first two together, and the last two together.
= (6x2 − 2x) + (9x − 3)
From the first pair we take out 2x.
From the second pair we take out 3.
Both leave the same bracket.
(6x2 − 2x) = 2x(3x − 1)
(9x − 3) = 3(3x − 1)
Now both parts have 3x − 1 in them.
= 2x(3x − 1) + 3(3x − 1)
4 Same bracket out
3x − 1 is in both parts, so we take it out once.
What is left, 2x + 3, goes in the other bracket.
ab + cb = b(a + c)
So we get (3x − 1)(2x + 3).
= (3x − 1)(2x + 3)
5 Check
Let's check: we multiply it back out.
Each part of the first bracket times each part of the second.
Check: (3x − 1)(2x + 3) = 6x2 + 9x − 2x − 3
= 6x2 + 7x − 3
We get 6x² + 7x − 3 again.
So (3x − 1)(2x + 3) is right!
Let's look back.
First: find two numbers.
Then: split the middle.
Then: group in pairs.
Then: same bracket out.
Last: check.
Answer = (3x − 1)(2x + 3)
▶ Watch it solved
