Factorising with negative terms

Factorising by taking a negative HCF

All numbers can have negative or positive factors

​Example (1): list all factors of 6 (pos and neg)

One possible list:
1, 6 or 2, 3
or
-1, -6 or -2, -3 (each of these pairs will multiply to give positive 6)

All numbers can have negative or positive factors

​Example (2): list all factors of -12

Each pair has + and - because multiplying unlike pairs gives a minus.
-1, 12 or 1, -12 or -2, 6 or 2, -6 or -3, 4 or 3, -4
All of these pairs when multiplied, give -12

Example 1 Factorise by taking a negative HCF

The first step is to find the HCF of -3x and +6

Multiple Choice

What is the negative HCF of -3x and +6?

• -3
• -2

• -1

• -6

Key tip!

​Factorising by taking out a negative HCF changes the sign

Key tip!

​Factorising: taking out a negative HCF changes the sign