# 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

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.

9x2 - 33x + 30 = 0

x = -6

x = 2/5

x = 5/3

x = 2

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

8x2 - 24x + 18 = 0

x = 2

x = -3/2

x = 1½

x = -2/3

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

8x2 + 2x - 3 = 0

x = ½

x = -½

x = -¾

x = ¾

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

16x2 - 16x - 5 = 0

x = 0

x = ¼

x = -¼

x = 5/4

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

4x2 - 12x - 72 = 0

x = 12

x = -3

x = -18

x = 6

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

20x2 + 7x - 3 = 0

x = -4

x = -3/5

x = ¼

x = 3/5

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

6x2 + 51x + 63 = 0

x = 4

x = 7

x = -7

x = -1½

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

144x2 - 25 = 0

x = -2.4

x = -5/12

x = 5/12

x = 2.4

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

64x2 - 96x - 64 = 0

x = 2

x = -½

x = ½

x = -2

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

60x2 - 130x - 50 = 0

x = 2.5

x = -1/3

x = 1

x = -3

• Question 1

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

9x2 - 33x + 30 = 0

x = 5/3
x = 2
EDDIE SAYS
3(3x-5)(x-2)=0
• Question 2

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

8x2 - 24x + 18 = 0

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

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

8x2 + 2x - 3 = 0

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

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

16x2 - 16x - 5 = 0

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

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

4x2 - 12x - 72 = 0

x = -3
x = 6
EDDIE SAYS
4(x-6)(x+3)=0
• Question 6

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

20x2 + 7x - 3 = 0

x = -3/5
x = ¼
EDDIE SAYS
(4x-1)(5x+3)=0
• Question 7

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

6x2 + 51x + 63 = 0

x = -7
x = -1½
EDDIE SAYS
3(2x+3)(x+7)=0
• Question 8

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

144x2 - 25 = 0

x = -5/12
x = 5/12
EDDIE SAYS
(12x-5)(12x+5)=0
• Question 9

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

64x2 - 96x - 64 = 0

x = 2
x = -½
EDDIE SAYS
32(x-2)(2x+1)=0
• Question 10

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

60x2 - 130x - 50 = 0

x = 2.5
x = -1/3
EDDIE SAYS
10(2x-5)(3x+1)=0
---- OR ----

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