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

2. 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)

3. 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

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

5. 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