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+ )

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

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!

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!

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!

𝒙 𝟐 −𝟓𝒙=𝟎

𝟒𝒙 𝟐 −𝟖𝒙=𝟎

𝟕 𝒙 𝟐 −𝟑𝒙=𝟎

𝟔 𝒙 𝟐 +𝟕𝒙=𝟎

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