Solving quadratics by factorising

The Maths Habit

Two numbers multiply to make 0.
What do you know about the numbers?

One of them must be 0

What is the value of x?

  1. x + 6 = 0

    x = −6

  2. x − 9 = 0

    x = 9

  3. 3x = 0

    x = 0

Quadratic equation
An equation with x2 as its highest power.
Solutions
The values of x that make it true.

(x + 2)(x + 5) = 0

x + 2 = 0   or   x + 5 = 0

(x + 3)(x + 4) = 0

  1. Solve (x + 9)(x − 2) = 0

    x = −9 or x = 2

  2. Solve (x − 5)(x − 8) = 0

    x = 5 or x = 8

  3. Solve x(x + 4) = 0

    x = 0 or x = −4

  4. Ali says the solutions of (x − 6)(x + 1) = 0 are x = −6 and x = 1. What has he done wrong? Find the right answer.

    x = 6 or x = −1

Factorise

x2 + 6x + 5 (x + 1)(x + 5)

x2 − 2x − 15 = 0

Solve

x2 + 8x + 15 = 0

×x+5
xx2+5x
+3+3x+15
(x + 3)(x + 5)= 0
↓
x + 3 = 0
x =−3
↓
x + 5 = 0
x =−5

Solve

x2 + 9x + 20 = 0

×x+5
xx2+5x
+4+4x+20
(x + 4)(x + 5)= 0
↓
x + 4 = 0
x =−4
↓
x + 5 = 0
x =−5

Solve

x2 + 8x + 15 = 0

×x+5
xx2+5x
+3+3x+15
(x + 3)(x + 5)= 0
↓
x + 3 = 0
x =−3
↓
x + 5 = 0
x =−5

Solve

x2 + 2x − 24 = 0

×x−4
xx2−4x
+6+6x−24
(x + 6)(x − 4)= 0
↓
x + 6 = 0
x =−6
↓
x − 4 = 0
x =4

Solving quadratics by factorising worksheet, page 1

Solving quadratics by factorising worksheet, page 2

Answer sheet

  1. Solve x2 + 5x = 0

    x = 0 or x = −5

  2. A rectangle is x + 3 cm long and x cm wide. Its area is 40 cm2. Find x.

    x = 5

  3. Solve x2 = 7x

    x2 − 7x = 0, x(x − 7) = 0, so x = 0 or x = 7

  1. Solve (x − 3)(x + 7) = 0

    x = 3 or x = −7

  2. Solve x2 − x − 20 = 0

    x = 5 or x = −4

  3. Solve x2 = 8x

    x = 0 or x = 8
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