Background Knowledge By the end of this lesson you will be able to explain/solve the following: 1.Difference of Two Squares 2.Perfect Squares 3.Sum & Product Type

Factorisation Algebraic factorisation is the reverse process of expansion

Factorisation

Worked Example 13

Exercise H

Worked Example 14

Exercise H

Factorisation By ‘Splitting’ The X-term An expression with three terms is called a trinomial. Quadratic trinomials can be written in the form: ax 2 + bx + c where the highest power is a squared term. To factorise a quadratic trinomial: factor pair of ac sum of b a) identify the factor pair of ac that has a sum of b breaking the x-term into two b) rewrite the expression by breaking the x-term into two terms using the factor pair from the previous step grouping c) factorise the resulting expression by grouping.

Worked Example

Exercise H

Worked Example 16

Exercise H

Worked Example 17

Exercise H

Completing the Square Consider factorising x 2 − 8x + 5 Can you find factors of 5 that add to −8? There are no integer factors but there are factors So far we have factorised quadratic trinomials where the factors have involved integers There are cases, however, where not only rational numbers are used, but also irrational numbers such as surds

Worked Example

Completing the Square