Introduction to factorisation (placing into brackets) Saturday, 21 September 2019

Example Rewrite 𝑥2+6𝑥+8 as a product of two brackets. [this is called factorisation] To factorise 𝑥2+6𝑥+8 we need two numbers which Multiply to give +8 Combine to give +6 For +8 the only possibilities are: 1 x 8 –1 x –8 2 x 4 ← this pair add to give +6 –2 x –4 Hence 𝑥2+6𝑥+8 = (𝑥+2)(𝑥+4)

Example Factorise each of the following 𝑥2+7𝑥+10 𝑥2−11𝑥+10 𝑥2+12𝑥+20 𝑥2+7𝑥+6 𝑥2+2𝑥−15 𝑥2+14𝑥+49 𝑥2+10𝑥+21 𝑥2−𝑥−12 𝑥2−2𝑥−35 𝑥2−13𝑥+22

Example Factorise each of the following 𝑥2−4𝑥−12 𝑥2−8𝑥+15 𝑥 2 +7𝑥−30

Example Factorise each of the following expressions a) 2 𝑥 2 +7𝑥+3 b) 2 𝑥 2 +5𝑥−12 c) 6 𝑎 2 +11𝑎+3 d) 4 𝑦 2 −12𝑦+5 e) 4 𝑚 2 +13𝑚−12 f) 15 𝑟 2 −16𝑟+4