Common factors

If you cannot remember what factors are, or how to find them, have another look at: Algebra / Common factors - Foundation.

When multiplying out 3(4x - 7), the rule was to multiply everything in the brackets by 3.

This gives 3(4x - 7) = 12x - 21

So, when asked to factorise 12x - 21 look for the Highest Common Factor (HCF) of 12 and 21 (in this case 3) and divide both terms by this number.

12x - 21 = 3(4x - 7)

Factorsing Quadratics

You can also factorise quadratic expressions. Eg x²+x can be factorised to x (x+1)

Example

Factorise 3p² - 6p

Solution

• 3p² means 3 x p x p, and 6p means 6 x p.
• The HCF of 3 and 6 is 3, and the HCF of p² and p is p, so we divide both terms by 3p:

3p² - 6p = 3p(p - 2)

Remember that most people find expanding brackets easier than factorising, so always check that your answer is correct by multiplying out and seeing whether you have what you started with.

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