Factorising
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Factorising
Factorising1) Look for a common factor
Factorising1) Look for a common factor
2) (i) 2 terms difference of two squares
Factorising1) Look for a common factor
2) (i) 2 terms difference of two squares sum/difference of two cubes
Factorising1) Look for a common factor
2) (i) 2 terms difference of two squares sum/difference of two cubes
(ii) 3 terms quadratic trinomial
Factorising1) Look for a common factor
2) (i) 2 terms difference of two squares sum/difference of two cubes
(ii) 3 terms quadratic trinomial
(iii) 4 terms grouping in pairs
1. Common Factorfactorising
= dividing by common factor
1. Common Factore.g. ( ) i ax bx
factorising=
dividing by common factor
1. Common Factore.g. ( ) i ax bx x a b
factorising=
dividing by common factor
1. Common Factore.g. ( ) i ax bx x a b
2( ) 5 10ii x x
factorising=
dividing by common factor
1. Common Factore.g. ( ) i ax bx x a b
2( ) 5 10ii x x 5 2x x
factorising=
dividing by common factor
1. Common Factore.g. ( ) i ax bx x a b
2( ) 5 10ii x x 5 2x x
( ) iii mx nx my ny
factorising=
dividing by common factor
1. Common Factore.g. ( ) i ax bx x a b
2( ) 5 10ii x x 5 2x x
( ) iii mx nx my ny x m n y m n
factorising=
dividing by common factor
1. Common Factore.g. ( ) i ax bx x a b
2( ) 5 10ii x x 5 2x x
( ) iii mx nx my ny x m n y m n
m n x y
factorising=
dividing by common factor
1. Common Factore.g. ( ) i ax bx x a b
2( ) 5 10ii x x 5 2x x
( ) iii mx nx my ny x m n y m n
m n x y
2 2a b a b a b
factorising=
dividing by common factor
2. Difference of Two Squares
1. Common Factore.g. ( ) i ax bx x a b
2( ) 5 10ii x x 5 2x x
( ) iii mx nx my ny x m n y m n
m n x y
2 2a b a b a b
factorising=
dividing by common factor
2. Difference of Two Squares
2e.g. ( ) 16 1i x
1. Common Factore.g. ( ) i ax bx x a b
2( ) 5 10ii x x 5 2x x
( ) iii mx nx my ny x m n y m n
m n x y
2 2a b a b a b
factorising=
dividing by common factor
2. Difference of Two Squares
2e.g. ( ) 16 1i x = 4 1 4 1x x
1. Common Factore.g. ( ) i ax bx x a b
2( ) 5 10ii x x 5 2x x
( ) iii mx nx my ny x m n y m n
m n x y
2 2a b a b a b
factorising=
dividing by common factor
2. Difference of Two Squares
2e.g. ( ) 16 1i x = 4 1 4 1x x 2( ) 3 75ii y
1. Common Factore.g. ( ) i ax bx x a b
2( ) 5 10ii x x 5 2x x
( ) iii mx nx my ny x m n y m n
m n x y
2 2a b a b a b
factorising=
dividing by common factor
2. Difference of Two Squares
2e.g. ( ) 16 1i x = 4 1 4 1x x 2( ) 3 75ii y 2=3 25y
1. Common Factore.g. ( ) i ax bx x a b
2( ) 5 10ii x x 5 2x x
( ) iii mx nx my ny x m n y m n
m n x y
2 2a b a b a b
factorising=
dividing by common factor
2. Difference of Two Squares
2e.g. ( ) 16 1i x = 4 1 4 1x x 2( ) 3 75ii y 2=3 25y
=3 5 5y y
1. Common Factore.g. ( ) i ax bx x a b
2( ) 5 10ii x x 5 2x x
( ) iii mx nx my ny x m n y m n
m n x y
2 2a b a b a b
factorising=
dividing by common factor
2. Difference of Two Squares
2e.g. ( ) 16 1i x = 4 1 4 1x x 2( ) 3 75ii y 2=3 25y
=3 5 5y y 2 2( ) 5 5iii x y x y
1. Common Factore.g. ( ) i ax bx x a b
2( ) 5 10ii x x 5 2x x
( ) iii mx nx my ny x m n y m n
m n x y
2 2a b a b a b
factorising=
dividing by common factor
2. Difference of Two Squares
2e.g. ( ) 16 1i x = 4 1 4 1x x 2( ) 3 75ii y 2=3 25y
=3 5 5y y 2 2( ) 5 5iii x y x y =5 x y x y x y
1. Common Factore.g. ( ) i ax bx x a b
2( ) 5 10ii x x 5 2x x
( ) iii mx nx my ny x m n y m n
m n x y
2 2a b a b a b
factorising=
dividing by common factor
2. Difference of Two Squares
2e.g. ( ) 16 1i x = 4 1 4 1x x 2( ) 3 75ii y 2=3 25y
=3 5 5y y 2 2( ) 5 5iii x y x y =5 x y x y x y
= 5x y x y
3. Quadratic Trinomiala) Monic Quadratic
2x a x b x a b x ab
3. Quadratic Trinomiala) Monic Quadratic
2x a x b x a b x ab
2e.g. ( ) 9 18i x x
3. Quadratic Trinomiala) Monic Quadratic
2x a x b x a b x ab
2e.g. ( ) 9 18i x x 189
3. Quadratic Trinomiala) Monic Quadratic
2x a x b x a b x ab
2e.g. ( ) 9 18i x x 189
6 3x x
3. Quadratic Trinomiala) Monic Quadratic
2x a x b x a b x ab
2e.g. ( ) 9 18i x x 189
6 3x x
2( ) 4 3ii t t
3. Quadratic Trinomiala) Monic Quadratic
2x a x b x a b x ab
2e.g. ( ) 9 18i x x 189
6 3x x
2( ) 4 3ii t t 34
3. Quadratic Trinomiala) Monic Quadratic
2x a x b x a b x ab
2e.g. ( ) 9 18i x x 189
6 3x x
2( ) 4 3ii t t 34
3 1t t
3. Quadratic Trinomiala) Monic Quadratic
2x a x b x a b x ab
2e.g. ( ) 9 18i x x 189
6 3x x
2( ) 4 3ii t t 34
3 1t t
2 2( ) 5 4iii x xy y
3. Quadratic Trinomiala) Monic Quadratic
2x a x b x a b x ab
2e.g. ( ) 9 18i x x 189
6 3x x
2( ) 4 3ii t t 34
3 1t t
2 2( ) 5 4iii x xy y 245y
y
3. Quadratic Trinomiala) Monic Quadratic
2x a x b x a b x ab
2e.g. ( ) 9 18i x x 189
6 3x x
2( ) 4 3ii t t 34
3 1t t
2 2( ) 5 4iii x xy y 245y
y 4x y x y
b) Splitting the Middle
b) Splitting the Middle
2e.g. ( ) 3 4 7i x x
b) Splitting the Middle
2e.g. ( ) 3 4 7i x x 214
7 3
Multiply the constant by the coefficient of x squared
b) Splitting the Middle
2e.g. ( ) 3 4 7i x x 214
7 3
Multiply the constant by the coefficient of x squared
23 3 7 7x x x
b) Splitting the Middle
2e.g. ( ) 3 4 7i x x 214
7 3
Multiply the constant by the coefficient of x squared
23 3 7 7x x x 3 1 7 1x x x
b) Splitting the Middle
2e.g. ( ) 3 4 7i x x 214
7 3
Multiply the constant by the coefficient of x squared
23 3 7 7x x x 3 1 7 1x x x
1 3 7x x
b) Splitting the Middle
2e.g. ( ) 3 4 7i x x 214
7 3
Multiply the constant by the coefficient of x squared
23 3 7 7x x x 3 1 7 1x x x
1 3 7x x
2( ) 2 5 12ii x x
b) Splitting the Middle
2e.g. ( ) 3 4 7i x x 214
7 3
Multiply the constant by the coefficient of x squared
23 3 7 7x x x 3 1 7 1x x x
1 3 7x x
2( ) 2 5 12ii x x 245
b) Splitting the Middle
2e.g. ( ) 3 4 7i x x 214
7 3
Multiply the constant by the coefficient of x squared
23 3 7 7x x x 3 1 7 1x x x
1 3 7x x
2( ) 2 5 12ii x x 245
22 8 3 12x x x
b) Splitting the Middle
2e.g. ( ) 3 4 7i x x 214
7 3
Multiply the constant by the coefficient of x squared
23 3 7 7x x x 3 1 7 1x x x
1 3 7x x
2( ) 2 5 12ii x x 245
22 8 3 12x x x
2 4 3 4x x x
b) Splitting the Middle
2e.g. ( ) 3 4 7i x x 214
7 3
Multiply the constant by the coefficient of x squared
23 3 7 7x x x 3 1 7 1x x x
1 3 7x x
2( ) 2 5 12ii x x 245
22 8 3 12x x x
2 4 3 4x x x
4 2 3x x
b) Splitting the Middle
2e.g. ( ) 3 4 7i x x 214
7 3
Multiply the constant by the coefficient of x squared
23 3 7 7x x x 3 1 7 1x x x
1 3 7x x
2( ) 2 5 12ii x x 245
22 8 3 12x x x
2 4 3 4x x x
4 2 3x x
Exercise 1C; 1e, 2f, 3d, 4ejo, 5adhkn, 6ace etc, 7ace etc, 8*bdfij
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