**Solving Quadratics by factorising**

Starter

Expand the following expressions:

(a) x(x - 4)

(b) (x - 4)(x + 2)

(c) (x - 3)(x + 3)

Factorising to solve quadratics

Solve the equations:

(a) x - 4x = 0

(b) x - 2x = 8

(c) x - 9 = 0

Starter

Expand the following expressions:

(a) x(x - 4)

= x - 4x

(b) (x - 4)(x + 2)

= x - 2x - 8

(c) (x - 3)(x + 3)

= x - 9

2

2

2

2

2

2

Factorising to solve quadratics

Solve the equations by factorising:

(a) x - 4x = 0

(b) x - 2x - 8 = 0

(c) x - 9 = 0

2

2

2

x(x - 4) = 0

x= 0 and x - 4 = 0

x = 0 and x = 4

(x - 4)(x + 2) = 0

x - 4 = 0 and x + 2 = 0

x = 4 and x = -2

(x - 3)(x + 3) = 0

x - 3 = 0 and x + 3 = 0

x = 3 and x = - 3

Activity

Which of these equations has only one distinct solution?

Activity

Which of these equations has only one distinct solution?

Rearrange and then solve these quadratics.

x = -4, x = 3

x = - 6

x = 3, x = -3

x = 4

x = 7, x = 4

x = -15, x = -3

f = 8, f = 2

d = -13, d = -1

b = 12, b = -3

n= -1, n = -

**Key**

Examples

Examples

**Activity**

Answers

Answers

**Worked**

Example

Example

**Activities**

**Solve quadratic equations by factorising.**

Activity

Write down all pairs of numbers

a

and

b

so that:

(a) a x b = 12

(b) a x b = 20

(c) a x b = 60

(d) a x b = 0

Rearrange and then solve these quadratics.

Activity

Write down all pairs of numbers

a

and

b

so that:

(a) a x b = 12 Can't.

(b) a x b = 20 Can't.

(c) a x b = 60 Can't.

(d) a x b = 0 a = 0, b = 0.

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