# Solving Quadratic Equations by Factorising (2)

In this worksheet, students solve quadratic equations by factorising.

Key stage:  KS 4

Curriculum topic:  Algebra

Curriculum subtopic:  Solve Quadratic Equations by Factorising

Difficulty level:

### QUESTION 1 of 10

A quadratic expression can sometimes be factorised.  If the product of these factors is zero, it is easy to solve the associated quadratic equation.

We use the fact that, if ab = 0, then we know that either a = 0 or b = 0 (or both).

Example

Solve for x:

20x2 + 20x - 15 = 0

Answer

20x2 + 20x - 15 = 0

Notice that each term is divisible by 5, so divide each term by 5 to get

4x2 + 4x - 3 = 0

Factorise the left hand side.

(2x + 3) (2x - 1) = 0

If (2x + 3) (2x - 1) = 0

then either (2x + 3) = 0 or (2x - 1) = 0

Write each equation separately.

2x + 3 = 0                                   2x - 1 = 0

Subtract 3 from both sides.                  Add 1 to both sides.

2x + 3 - 3 = 0 - 3                        2x - 1 + 1 = 0 + 1

Simplify.

2x = -3                                        2x = 1

Divide both sides by 2.                        Divide both sides by 2

x = -3/2                                        x = 1/2

Solution is:

x = -1½ or x = ½

Solve the quadratic equation by selecting all the correct solutions below.

2x2 - 6x - 36 = 0

x = -18

x = -3

x = 12

x = 6

Solve the quadratic equation by selecting all the correct solutions below.

4x2 + 11x - 3 = 0

x = ¼

x = -3

x = -4

x = 3

Solve the quadratic equation by selecting all the correct solutions below.

2x2 + 17x + 21 = 0

x = -1½

x = -7

x = 7

x = 4

Solve the quadratic equation by selecting all the correct solutions below.

4x2 - 19x - 5 = 0

x = 5

x = -¼

x = ¼

x = 0

Solve the quadratic equation by selecting all the correct solutions below.

8x2 + 2x - 3 = 0

x = ¾

x = -¾

x = -½

x = ½

Solve the quadratic equation by selecting all the correct solutions below.

4x2 - 12x + 9 = 0

x = 1½

x = -3/2

x = 2

x = -2/3

Solve the quadratic equation by selecting all the correct solutions below.

6x2 - 27x + 30 = 0

x = 2½

x = 2/5

x = -6

x = 2

Solve the quadratic equation by selecting all the correct solutions below.

4x2 - 25 = 0

x = 2/5

x = 2.5

x = -2.5

x = -2/5

Solve the quadratic equation by selecting all the correct solutions below.

32x2 - 48x - 32 = 0

x = ½

x = -½

x = 2

x = -2

Solve the quadratic equation by selecting all the correct solutions below.

100x2 - 400x - 500 = 0

x = 1

x = 5

x = -1

x = -5

• Question 1

Solve the quadratic equation by selecting all the correct solutions below.

2x2 - 6x - 36 = 0

CORRECT ANSWER
x = -3
x = 6
EDDIE SAYS
2(x-6)(x+3)=0
• Question 2

Solve the quadratic equation by selecting all the correct solutions below.

4x2 + 11x - 3 = 0

CORRECT ANSWER
x = ¼
x = -3
EDDIE SAYS
(4x-1)(x+3)=0
• Question 3

Solve the quadratic equation by selecting all the correct solutions below.

2x2 + 17x + 21 = 0

CORRECT ANSWER
x = -1½
x = -7
EDDIE SAYS
(2x+3)(x+7)=0
• Question 4

Solve the quadratic equation by selecting all the correct solutions below.

4x2 - 19x - 5 = 0

CORRECT ANSWER
x = 5
x = -¼
EDDIE SAYS
(x-5)(4x+1)=0
• Question 5

Solve the quadratic equation by selecting all the correct solutions below.

8x2 + 2x - 3 = 0

CORRECT ANSWER
x = -¾
x = ½
EDDIE SAYS
(2x-1)(4x+3)=0
• Question 6

Solve the quadratic equation by selecting all the correct solutions below.

4x2 - 12x + 9 = 0

CORRECT ANSWER
x = 1½
EDDIE SAYS
(2x-3)(2x-3)=0
• Question 7

Solve the quadratic equation by selecting all the correct solutions below.

6x2 - 27x + 30 = 0

CORRECT ANSWER
x = 2½
x = 2
EDDIE SAYS
3(2x-5)(x-2)=0
• Question 8

Solve the quadratic equation by selecting all the correct solutions below.

4x2 - 25 = 0

CORRECT ANSWER
x = 2.5
x = -2.5
EDDIE SAYS
(2x-5)(2x+5)=0
• Question 9

Solve the quadratic equation by selecting all the correct solutions below.

32x2 - 48x - 32 = 0

CORRECT ANSWER
x = -½
x = 2
EDDIE SAYS
16(x-2)(2x+1)=0
• Question 10

Solve the quadratic equation by selecting all the correct solutions below.

100x2 - 400x - 500 = 0

CORRECT ANSWER
x = 5
x = -1
EDDIE SAYS
100(x-5)(x+1)=0
---- OR ----

Sign up for a £1 trial so you can track and measure your child's progress on this activity.

### What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.

Start your £1 trial