     # Factorising harder quadratic expressions - Chatterton 2014-12-08آ  Factorising harder quadratic expressions

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1 | P a g e 0 1 4 2 3 3 4 0 0 7 6 0 7 7 5 9 5 0 1 6 2 9

Question 1 Factorise 2𝑥2 + 9𝑥 + 9

Question 11 Factorise 8𝑥2 + 14𝑥 + 3

Question 2 Factorise 6𝑥2 + 11𝑥 + 3

Question 12 Factorise 5𝑥2 − 17𝑥 + 6

Question 3 Factorise 𝑥2 + 9𝑥 + 14

Question 13 Factorise 𝑥2 − 9𝑥 + 20

Question 4 Factorise 3𝑥2 + 5𝑥 − 2

Question 14 Factorise 6𝑥2 − 𝑥 − 15

Question 5 Factorise 2𝑥2 − 5𝑥 − 3

Question 15 Factorise 2𝑥2 − 13𝑥 − 7

Question 6 Factorise 2𝑥2 + 𝑥 − 10

Question 16 Factorise 8𝑥2 − 2𝑥 − 1

Question 7 Factorise 4𝑥2 − 4𝑥 − 3

Question 17 Factorise 2𝑥2 − 11𝑥 + 12

Question 8 Factorise 6𝑥2 − 11𝑥 + 4

Question 18 Factorise 3𝑥2 − 11𝑥 − 4

Question 9 Factorise 5𝑥2 + 4𝑥 − 1

Question 19 Factorise 2𝑥2 − 𝑥 − 15

Question 10 Factorise 3𝑥2 − 13𝑥 + 14

Question 20 Factorise 12𝑥2 − 32𝑥 + 5

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WORKINGS

Question 1

Factorise 2𝑥2 + 9𝑥 + 9 Label 𝑎 = 2, 𝑏 = 9, 𝑐 = 9 Multiply a by c 2 x 9 = 18 The two numbers must multiply to give +18 but add to give b (and 𝑏 = +9) The two numbers will be +3 and +6 Rewrite the quadratic splitting 9𝑥 into 3𝑥 and 6𝑥 2𝑥2 + 3𝑥 + 6𝑥 + 9 Factorise in pairs (partitioning) 𝑥(2𝑥 + 3) + 3(2𝑥 + 3) You should have the same in both brackets – which we do Factorise again (2𝑥 + 3)(𝑥 + 3)

18 1 18 2 9 3 6

Question 2

Factorise 6𝑥2 + 11𝑥 + 3 Label 𝑎 = 6, 𝑏 = 11, 𝑐 = 3 Multiply a by c 6 x 3 = 18 The two numbers must multiply to give +18 but add to give b (and 𝑏 = +11) The two numbers will be +2 and +9 Rewrite the quadratic splitting 9𝑥 into 3𝑥 and 6𝑥 6𝑥2 + 2𝑥 + 9𝑥 + 3 Factorise in pairs (partitioning) 2𝑥(3𝑥 + 1) + 3(3𝑥 + 1) You should have the same in both brackets – which we do Factorise again (3𝑥 + 1)(2𝑥 + 3)

18 1 18 2 9 3 6

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Question 3

Factorise 𝑥2 + 9𝑥 + 14 This is actually an easier quadratic to factorise as 𝑎 = 1 but we can use the same method for factorising all quadratics Label 𝑎 = 1, 𝑏 = 9, 𝑐 = 14 Multiply a by c 1 x 14 = 14 The two numbers must multiply to give +14 but add to give b (and 𝑏 = +9) The two numbers will be +2 and +7 Rewrite the quadratic splitting 9𝑥 into 2𝑥 and 7𝑥 𝑥2 + 2𝑥 + 7𝑥 + 14 Factorise in pairs (partitioning) 𝑥(𝑥 + 2) + 7(𝑥 + 2) You should have the same in both brackets – which we do Factorise again (𝑥 + 2)(𝑥 + 7)

14 1 14 2 7

Question 4

Factorise 3𝑥2 + 5𝑥 − 2 Label 𝑎 = 3, 𝑏 = 5, 𝑐 = −2 Multiply a by c 3 x − 2 = −6 The two numbers must multiply to give −6 but add to give b (and 𝑏 = +5) The two numbers will be −1 and +6 Rewrite the quadratic splitting 5𝑥 into−1𝑥 and 6𝑥 3𝑥2 − 1𝑥 + 6𝑥 − 2 Factorise in pairs (partitioning) 𝑥(3𝑥 − 1) + 2(3𝑥 − 1) You should have the same in both brackets – which we do Factorise again (3𝑥 − 1)(𝑥 + 2)

-6 1 6 2 3

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Question 5

Factorise 2𝑥2 − 5𝑥 − 3 Label 𝑎 = 2, 𝑏 = −5, 𝑐 = −3 Multiply a by c 2 x − 3 = −6 The two numbers must multiply to give −6 but add to give b (and 𝑏 = −5) The two numbers will be −6 and +1 Rewrite the quadratic splitting −5𝑥 into−6𝑥 and 1𝑥 2𝑥2 − 6𝑥 + 1𝑥 − 3 Factorise in pairs (partitioning) 2𝑥(𝑥 − 3) + 1(𝑥 − 3) You should have the same in both brackets – which we do Factorise again (𝑥 − 3)(2𝑥 + 1)

-6 1 6 2 3

Question 6

Factorise 2𝑥2 + 𝑥 − 10 Label 𝑎 = 2, 𝑏 = 1, 𝑐 = −10 Multiply a by c 2 x − 10 = −20 The two numbers must multiply to give −20 but add to give b (and 𝑏 = +1) The two numbers will be −4 and +5 Rewrite the quadratic splitting 𝑥 into−4𝑥 and 5𝑥

2𝑥2 − 4𝑥 + 5𝑥 − 10 Factorise in pairs (partitioning) 2𝑥(𝑥 − 2) + 5(𝑥 − 2) You should have the same in both brackets – which we do Factorise again (𝑥 − 2)(2𝑥 + 5)

-20 1 20 2 10 4 5

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Question 7

Factorise 4𝑥2 − 4𝑥 − 3 Label 𝑎 = 4, 𝑏 = −4, 𝑐 = −3 Multiply a by c 4 x − 3 = −12 The two numbers must multiply to give +12 but add to give b (and 𝑏 = −4) The two numbers will be −6 and +2 Rewrite the quadratic splitting 𝑥 into−6𝑥 and 2𝑥 4𝑥2 − 6𝑥 + 2𝑥 − 3 Factorise in pairs (partitioning) 2𝑥(2𝑥 − 3) + 1(2𝑥 − 3) You should have the same in both brackets – which we do Factorise again (2𝑥 − 3)(2𝑥 + 1)

-12 1 12 2 6 3 4

Question 8

Factorise 6𝑥2 − 11𝑥 + 4 Label 𝑎 = 6, 𝑏 = −11, 𝑐 = 4 Multiply a by c 6 x 4 = 24 The two numbers must multiply to give +24 but add to give b (and 𝑏 = −11) The two numbers will be −3 and −8 Rewrite the quadratic splitting 𝑥 into−2𝑥 and −8𝑥

6𝑥2 − 3𝑥 − 8𝑥 + 4 Factorise in pairs (partitioning) 3𝑥(2𝑥 − 1) − 4(2𝑥 − 1) You should have the same in both brackets – which we do Factorise again (2𝑥 − 1)(3𝑥 − 4)

24 1 24 2 12 3 8 4 6

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Question 9

Factorise 5𝑥2 + 4𝑥 − 1 Label 𝑎 = 5, 𝑏 = 4, 𝑐 = −1 Multiply a by c 5 x − 1 = −5 The two numbers must multiply to give −5 but add to give b (and 𝑏 = +4) The two numbers will be −1 and +5 Rewrite the quadratic splitting 𝑥 into−4𝑥 and 5𝑥 5𝑥2 − 1𝑥 + 5𝑥 − 1 Factorise in pairs (partitioning) 𝑥(5𝑥 − 1) + 1(5𝑥 − 1) You should have the same in both brackets – which we do Factorise again (5𝑥 − 1)(𝑥 + 1)

-5 1 5

Question 10

Factorise 3𝑥2 − 13𝑥 + 14 Label 𝑎 = 3, 𝑏 = −13, 𝑐 = 14 Multiply a by c 3 x 14 = 42 The two numbers must multiply to give +42 but add to give b (and 𝑏 = −13) The two numbers will be −6 and −7 Rewrite the quadratic splitting 𝑥 into−6𝑥 and −7𝑥

3𝑥2 − 6𝑥 − 7𝑥 + 14 Factorise in pairs (partitioning) 3𝑥(𝑥 − 2) − 7(𝑥 − 2) You should have the same in both brackets – which we do Factorise again (𝑥 − 2)(3𝑥 − 7)

42 1 42 2 21 3 14 6 7

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Question 11

Factorise 8𝑥2 + 14𝑥 + 3 Label 𝑎 = 8, 𝑏 = 14, 𝑐 = 3 Multiply a by c 8 x 3 = 24 The two numbers must multiply to give +24 but add to give b (and 𝑏 = +14) The two numbers will be +2 and +12 Rewrite the quadratic splitting 14𝑥 into+2𝑥 and+12𝑥 8𝑥2 + 2𝑥 + 12𝑥 + 3 Factorise in pairs (partitioning) 2𝑥(4𝑥 + 1) + 3(4𝑥 + 1) You should have the same in both brackets – which we do Factorise again (4𝑥 + 1)(2𝑥 + 3)

24 1 24 2 12 3 8 4 6

Question 12

Factorise 5𝑥2 − 17𝑥 + 6 Label 𝑎 = 5, 𝑏 = −17, 𝑐 = 6 Multiply a by c 5 x 6 = 30 The two numbers must multiply to give +30 but add to give b (and 𝑏 = −17) The two numbers will be −2 and −15 Rewrite the quadratic splitting −17𝑥 into−2𝑥 and −15𝑥

5𝑥2 − 2𝑥 − 15𝑥 + 6 Factorise in pairs (partitioning) 𝑥(5𝑥 − 2) − 3(5𝑥 − 2) You should have the same in both brackets – which we do Factorise again (5𝑥 − 2)(𝑥 − 3)

30 1 30 2 15 3 10 5 6

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Question 13

Factorise 𝑥2 − 9𝑥 + 20 This is actually an easier quadratic to factorise as 𝑎 = 1 but we can use the same method for factorising all quadratics Label 𝑎 = 1, 𝑏 = −9, 𝑐 = 20 Multiply a by c 1 x 20 = 20 The two numbers must multiply to give +20 but add to give b (and 𝑏 = −9) The two numbers will be −4 and −5 Rewrite the quadratic splitting −9𝑥 in

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