11 X1 T01 03 factorising (2010)

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