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IGCSE  Factorisation Dr J Frost (jfrost@tiffin.kingston.sch.uk) IGCSE  Factorisation Dr J Frost (jfrost@tiffin.kingston.sch.uk)

IGCSE Factorisation Dr J Frost (jfrost@tiffin.kingston.sch.uk) - PowerPoint Presentation

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IGCSE Factorisation Dr J Frost (jfrost@tiffin.kingston.sch.uk) - PPT Presentation

Last modified 22 nd August 2015 Objectives from the specification RECAP   What makes this topic Further Maths ey 1 Sometimes require multiple factorisation steps eg combo of common factordifference of two squares ID: 708011

fully factorise term paper factorise fully paper term factorisation require divisible common squares guessing

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Slide1

IGCSE Factorisation

Dr J Frost (jfrost@tiffin.kingston.sch.uk)

Last modified

: 22

nd August 2015

Objectives: (from the specification)Slide2

RECAP

 

?

?

?

?Slide3

What makes this topic Further Maths-

ey

?

#1:

Sometimes require multiple factorisation steps (e.g. combo of common factor/difference of two squares)

#2:

Sometimes require ‘intelligent guessing’ of brackets.

#3:

Sometimes require ‘

refactorisation

’ of expressions not fully expanded.Slide4

#1

:: Multi-step factorisations

Factorising out single term:

 

1

Simple quadratic factorisation:

 

2

Difference Of Two Squares:

 

3

Splitting Middle Term:

 

4

Pairwise:

 

5

Sometimes we can apply multiple types of factorisation. Which do you think we can use for the following?

Bro Tip

: Always check first whether there’s a common term.

 

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?Slide5

Test Your Understanding

Fully factorise the following:

 

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?

?Slide6

#2

:: ‘Intelligent Guessing’

(or as I sometimes call it, ‘Going Commando’)

Sometimes your best bet is just simply ‘guessing’ the brackets, by considering what terms you’d get in your expansion.

 

Think what terms would multiply to get

. And which to give

. Guess then check it works.

Although splitting the middle term still actually works!

 

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?Slide7

Test Your Understanding

Factorise the following:

 

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?Slide8

#3

:: ‘

Refactorising

Sometimes parts of the expressions are factorised in some way.

This may require us to expand everything out and factorise from scratch, but sometimes we can factorise more easily without expanding.

 

Just identify a common term to factor out:

We may have the difference of two squares:

 

(Although some students might feel more comfortable just expanding that one out first)

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Test Your Understanding

[June 2012 Paper 1] Factorise the following:

 

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Factorise the following:

 

?Slide10

Exercises

Fully factorise the following:

Factorise

Factorise

[Jan 2013 Paper 2]

Factorise fully

Given

and

using your answer to part (a) to find the values of

[Set 3 Paper 2] (a) Factorise

(b) Hence or otherwise solve

 

Factorise

[Set 3 Paper 2] (a) Simplify

(b) Hence factorise fully

Factorise fully

is an integer greater than 1.

Explain why

is divisible by 6.

At least one of

must be divisible by 2, and exactly one of them will be divisible by 3.

[Set 4 Paper 2] Factorise

fully

:

Factorise

 

1

2

3

5

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