11 x1 t01 03 factorising (2010)
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![Page 1: 11 X1 T01 03 factorising (2010)](https://reader034.vdocuments.us/reader034/viewer/2022042601/5481a771b4af9f820d8b459d/html5/thumbnails/1.jpg)
Factorising
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Factorising1) Look for a common factor
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Factorising1) Look for a common factor
2) (i) 2 terms difference of two squares
![Page 4: 11 X1 T01 03 factorising (2010)](https://reader034.vdocuments.us/reader034/viewer/2022042601/5481a771b4af9f820d8b459d/html5/thumbnails/4.jpg)
Factorising1) Look for a common factor
2) (i) 2 terms difference of two squares sum/difference of two cubes
![Page 5: 11 X1 T01 03 factorising (2010)](https://reader034.vdocuments.us/reader034/viewer/2022042601/5481a771b4af9f820d8b459d/html5/thumbnails/5.jpg)
Factorising1) Look for a common factor
2) (i) 2 terms difference of two squares sum/difference of two cubes
(ii) 3 terms quadratic trinomial
![Page 6: 11 X1 T01 03 factorising (2010)](https://reader034.vdocuments.us/reader034/viewer/2022042601/5481a771b4af9f820d8b459d/html5/thumbnails/6.jpg)
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
![Page 7: 11 X1 T01 03 factorising (2010)](https://reader034.vdocuments.us/reader034/viewer/2022042601/5481a771b4af9f820d8b459d/html5/thumbnails/7.jpg)
1. Common Factorfactorising
= dividing by common factor
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1. Common Factore.g. ( ) i ax bx
factorising=
dividing by common factor
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1. Common Factore.g. ( ) i ax bx x a b
factorising=
dividing by common factor
![Page 10: 11 X1 T01 03 factorising (2010)](https://reader034.vdocuments.us/reader034/viewer/2022042601/5481a771b4af9f820d8b459d/html5/thumbnails/10.jpg)
1. Common Factore.g. ( ) i ax bx x a b
2( ) 5 10ii x x
factorising=
dividing by common factor
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1. Common Factore.g. ( ) i ax bx x a b
2( ) 5 10ii x x 5 2x x
factorising=
dividing by common factor
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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
![Page 13: 11 X1 T01 03 factorising (2010)](https://reader034.vdocuments.us/reader034/viewer/2022042601/5481a771b4af9f820d8b459d/html5/thumbnails/13.jpg)
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
![Page 14: 11 X1 T01 03 factorising (2010)](https://reader034.vdocuments.us/reader034/viewer/2022042601/5481a771b4af9f820d8b459d/html5/thumbnails/14.jpg)
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
![Page 15: 11 X1 T01 03 factorising (2010)](https://reader034.vdocuments.us/reader034/viewer/2022042601/5481a771b4af9f820d8b459d/html5/thumbnails/15.jpg)
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
![Page 16: 11 X1 T01 03 factorising (2010)](https://reader034.vdocuments.us/reader034/viewer/2022042601/5481a771b4af9f820d8b459d/html5/thumbnails/16.jpg)
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
![Page 17: 11 X1 T01 03 factorising (2010)](https://reader034.vdocuments.us/reader034/viewer/2022042601/5481a771b4af9f820d8b459d/html5/thumbnails/17.jpg)
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
![Page 18: 11 X1 T01 03 factorising (2010)](https://reader034.vdocuments.us/reader034/viewer/2022042601/5481a771b4af9f820d8b459d/html5/thumbnails/18.jpg)
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
![Page 19: 11 X1 T01 03 factorising (2010)](https://reader034.vdocuments.us/reader034/viewer/2022042601/5481a771b4af9f820d8b459d/html5/thumbnails/19.jpg)
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
![Page 20: 11 X1 T01 03 factorising (2010)](https://reader034.vdocuments.us/reader034/viewer/2022042601/5481a771b4af9f820d8b459d/html5/thumbnails/20.jpg)
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
![Page 21: 11 X1 T01 03 factorising (2010)](https://reader034.vdocuments.us/reader034/viewer/2022042601/5481a771b4af9f820d8b459d/html5/thumbnails/21.jpg)
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
![Page 22: 11 X1 T01 03 factorising (2010)](https://reader034.vdocuments.us/reader034/viewer/2022042601/5481a771b4af9f820d8b459d/html5/thumbnails/22.jpg)
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
![Page 23: 11 X1 T01 03 factorising (2010)](https://reader034.vdocuments.us/reader034/viewer/2022042601/5481a771b4af9f820d8b459d/html5/thumbnails/23.jpg)
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
![Page 24: 11 X1 T01 03 factorising (2010)](https://reader034.vdocuments.us/reader034/viewer/2022042601/5481a771b4af9f820d8b459d/html5/thumbnails/24.jpg)
3. Quadratic Trinomiala) Monic Quadratic
2x a x b x a b x ab
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3. Quadratic Trinomiala) Monic Quadratic
2x a x b x a b x ab
2e.g. ( ) 9 18i x x
![Page 26: 11 X1 T01 03 factorising (2010)](https://reader034.vdocuments.us/reader034/viewer/2022042601/5481a771b4af9f820d8b459d/html5/thumbnails/26.jpg)
3. Quadratic Trinomiala) Monic Quadratic
2x a x b x a b x ab
2e.g. ( ) 9 18i x x 189
![Page 27: 11 X1 T01 03 factorising (2010)](https://reader034.vdocuments.us/reader034/viewer/2022042601/5481a771b4af9f820d8b459d/html5/thumbnails/27.jpg)
3. Quadratic Trinomiala) Monic Quadratic
2x a x b x a b x ab
2e.g. ( ) 9 18i x x 189
6 3x x
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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
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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
![Page 30: 11 X1 T01 03 factorising (2010)](https://reader034.vdocuments.us/reader034/viewer/2022042601/5481a771b4af9f820d8b459d/html5/thumbnails/30.jpg)
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
![Page 31: 11 X1 T01 03 factorising (2010)](https://reader034.vdocuments.us/reader034/viewer/2022042601/5481a771b4af9f820d8b459d/html5/thumbnails/31.jpg)
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
![Page 32: 11 X1 T01 03 factorising (2010)](https://reader034.vdocuments.us/reader034/viewer/2022042601/5481a771b4af9f820d8b459d/html5/thumbnails/32.jpg)
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
![Page 33: 11 X1 T01 03 factorising (2010)](https://reader034.vdocuments.us/reader034/viewer/2022042601/5481a771b4af9f820d8b459d/html5/thumbnails/33.jpg)
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
![Page 34: 11 X1 T01 03 factorising (2010)](https://reader034.vdocuments.us/reader034/viewer/2022042601/5481a771b4af9f820d8b459d/html5/thumbnails/34.jpg)
b) Splitting the Middle
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b) Splitting the Middle
2e.g. ( ) 3 4 7i x x
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b) Splitting the Middle
2e.g. ( ) 3 4 7i x x 214
7 3
Multiply the constant by the coefficient of x squared
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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
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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
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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
![Page 40: 11 X1 T01 03 factorising (2010)](https://reader034.vdocuments.us/reader034/viewer/2022042601/5481a771b4af9f820d8b459d/html5/thumbnails/40.jpg)
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
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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
![Page 42: 11 X1 T01 03 factorising (2010)](https://reader034.vdocuments.us/reader034/viewer/2022042601/5481a771b4af9f820d8b459d/html5/thumbnails/42.jpg)
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
![Page 43: 11 X1 T01 03 factorising (2010)](https://reader034.vdocuments.us/reader034/viewer/2022042601/5481a771b4af9f820d8b459d/html5/thumbnails/43.jpg)
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
![Page 44: 11 X1 T01 03 factorising (2010)](https://reader034.vdocuments.us/reader034/viewer/2022042601/5481a771b4af9f820d8b459d/html5/thumbnails/44.jpg)
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
![Page 45: 11 X1 T01 03 factorising (2010)](https://reader034.vdocuments.us/reader034/viewer/2022042601/5481a771b4af9f820d8b459d/html5/thumbnails/45.jpg)
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