Starter Revision Worksheet

Factorising is the opposite of expanding – putting brackets back into the expression Note 7: Factorising Brackets

Common Factor  Look for the highest common factor in the numbers and the lowest power for each common letter  Place them outside the brackets

+ () This needs to be a common factor that appears in both terms. Choose 3 3 Now think  ? gives 3a a Now think  ? gives 6 2 3a + 6 = Answer: 3a + 6 = 3(a + 2) Finally…..Check by expanding 3(a + 2) to make sure it is equal to 3a + 6.

Example 2 Factorise 3c + c 2 3c + c 2 = + () This needs to be a common factor that appears in both terms. Pick the BIGGEST! c Now think..... c  ? gives 3c 3 Now think..... c  ? gives c 2 c

Example 3 Factorise 12ab 2 – 9a 2 bc 12ab 2 – 9a 2 bc = – () This needs to be a common factor that appears in both terms. Pick the BIGGEST! 3ab Now think ab  ? gives 12ab 2 4b4b Now think ab  ? Gives 9a 2 bc 3ac

To factorise an equation in the form x 2 + bx + c  List the factor pairs of c  Look for the pair that add to b  Place in brackets (x ___) (x ___) Quadratics

Factorise x x + 24 Examples: = (x + 3)(x + 8) Factorise x 2 + x = (x - 3)(x + 4)

If there is NO middle term – it is the difference between two squares. Example: Factorise x 2 – 64 = 16 – 4a 2 = 25x 2 – 36y 2 = (x – 8)(x + 8) (5x – 6y)(5x + 6y) (4 – 2a)(4 + 2a)

Some quadratic expressions have a common factor and the two factors in brackets. Example: Factorise 3x 2 – 3x - 18 = 3(x 2 - x - 6) 3(x – 3)(x + 2)

Page 47 Exercise I and J