Example 2: Factorise 6x2 + 12. x – Solution: We need to find two numbers that multiply to make 6 × -12 = -72 and add to make 1. These two numbers are -8 and 9. Therefore, 6x2 + 12 = 6x2 - 8x + 9x 12 x – – = 2x(3x 4) + 3(3x 4) (the two brackets must be identical) – – = (3x 4)(2x + 3) – Difference of two squares: Factorising quadratics of the form Remember that = (x + a)(x a). – Therefore: Also notice that: and Factorising by pairing We can factorise expressions like using the method of factorising by pairing: = + 1(2x + (factorise front and back pairs, ensuring both x(2x y) y) – brackets are identical) = (2x + 1) y)(x – If you need more help with factorising, you can download a booklet from this website: Exercise B Factorise 1) 2) 3) 4) (factorise by taking out a common factor) 5) 6)
Example 2: Factorise 6x2 + x – 12. Solution: We need to find two numbers that multiply to make 6 × -12 = -72 and add to make 1. These two numbers are -8 and 9. Therefore, 6x2 + x – 12 = 6x2 - 8x + 9x – 12 = 2x(3x – 4) + 3(3x – 4) (the two brackets must be identical) = (3x – 4)(2x + 3) Difference of two squares: Factorising quadratics of the form Remember that = (x + a)(x – a). Therefore: Also notice that: and Factorising by pairing We can factorise expressions like using the method of factorising by pairing: = x(2x + y) – 1(2x + y) (factorise front and back pairs, ensuring both brackets are identical) = (2x + y)(x – 1) If you need more help with factorising, you can download a booklet from this website: Exercise B Factorise 1) 2) 3) 4) (factorise by taking out a common factor) 5) 6)