1. Two Types of Factorising
by taking out a common factor
Factorising
Quadratic Expressions
What’s common?
What’s left?
𝒙 𝟐 +𝒃𝒙+𝒄
(𝒙+ )(𝒙+ )

2. So far, we have solved equations of the form:
𝑥+1 𝑥+2 =0 𝐿𝐻𝑆 𝑎𝑙𝑟𝑒𝑎𝑑𝑦 𝑓𝑎𝑐𝑡𝑜𝑟𝑖𝑠𝑒𝑑
𝑥 2 +3𝑥+2=0 𝑁𝑒𝑒𝑑 𝑡𝑜 𝑓𝑎𝑐𝑡𝑜𝑟𝑖𝑠𝑒 𝐿𝐻𝑆 𝑓𝑖𝑟𝑠𝑡
TODAY:
We will also solve equations of the form:
𝒙 𝟐 −𝟐𝒙=𝟎

3. 𝒙 𝟐 −𝟐𝒙=𝟎 𝑥 𝑥−2 =0 𝑥=0 𝑜𝑟 𝑥−2=0 𝑥=0 𝑜𝑟 𝑥=2
𝑥=0 𝑜𝑟 𝑥−2=0
𝑥=0 𝑜𝑟 𝑥=2
When the equation to solve is of this form one solution will always be 𝒙=𝟎!

4. 𝟐𝒙 𝟐 +𝟒𝒙=𝟎 2𝑥 𝑥+2 =0 2𝑥=0 𝑜𝑟 𝑥+2=0 𝑥=0 𝑜𝑟 𝑥=−2
2𝑥=0 𝑜𝑟 𝑥+2=0
𝑥=0 𝑜𝑟 𝑥=−2
When the equation to solve is of this form one solution will always be 𝒙=𝟎!

5. 𝟖𝒙 𝟐 −𝟓𝒙=𝟎 𝑥 8𝑥−5 =0 𝑥=0 𝑜𝑟 8𝑥−5=0 𝑥=0 𝑜𝑟 8𝑥=5 𝑥=0 𝑜𝑟 𝑥= 5 8
𝑥=0 𝑜𝑟 8𝑥−5=0
𝑥=0 𝑜𝑟 8𝑥=5
𝑥=0 𝑜𝑟 𝑥= 5 8
When the equation to solve is of this form
one solution will always be 𝒙=𝟎!

6. 𝒙 𝟐 −𝟓𝒙=𝟎

7. 𝟒𝒙 𝟐 −𝟖𝒙=𝟎

8. 𝟕 𝒙 𝟐 −𝟑𝒙=𝟎

9. 𝟔 𝒙 𝟐 +𝟕𝒙=𝟎

10. Homework: Factorising LHS by common factor
STP 9 Pg 225 Exercise 11d No. 2, 5, 8, 10