Solving Quadratic Equations by Factorising (1)

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:

4x2 - 17x - 15 = 0

4x2 - 17x - 15 = 0

Factorise the left hand side

(4x + 3) (x - 5) = 0

If (4x + 3) (x - 5) = 0

then either (4x + 3) = 0 or (x - 5) = 0

Write each equation separately.

4x + 3 = 0                                         x - 5 = 0

Subtract 3 from both sides.                      Add 5 to both sides.

4x + 3 - 3 = 0 - 3                              x - 5 + 5 = 0 + 5

Simplify.

4x = -3                                             x = 5

x = -3/4

Solution is:

x = -3/4 or x = 5

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

4x2 - 21x - 18 = 0

x = 6

x = -6

x = -3/4

x = 3/4

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

2x2 - 5x - 12 = 0

x = 3/2

x = -3/2

x = -4

x = 4

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

5x2 + 27x + 28 = 0

x = -4

x = 4

x = 7/5

x = -7/5

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

5x2 + x  = 0

x = 1/5

x = -1/5

x = ½

x = 0

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

3x2 + 23x - 8 = 0

x = 1/3

x = -8

x = -1

x = 8/3

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

9x2 + 24x + 16 = 0

x = -8/3

x = -4/3

x = 4

x = 16

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

5x2 - 31x + 30 = 0

x = 5

x = -5/6

x = -6

x = 6/5

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

4x2 + 17x - 15 = 0

x = 4/3

x = 3/4

x = 5

x = -5

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

6x2 + 17x - 28 = 0

x = -4

x = 7/6

x = 4

x = -6/7

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

3x2 - 290x - 1000 = 0

x = 100

x = -0.3

x = -10/3

x = -100

• Question 1

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

4x2 - 21x - 18 = 0

x = 6
x = -3/4
EDDIE SAYS
(x-6)(4x+3)=0
• Question 2

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

2x2 - 5x - 12 = 0

x = -3/2
x = 4
EDDIE SAYS
(x-4)(2x+3)=0
• Question 3

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

5x2 + 27x + 28 = 0

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

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

5x2 + x  = 0

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

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

3x2 + 23x - 8 = 0

x = 1/3
x = -8
EDDIE SAYS
(3x-1)(x+8)=0
• Question 6

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

9x2 + 24x + 16 = 0

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

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

5x2 - 31x + 30 = 0

x = 5
x = 6/5
EDDIE SAYS
(5x-6)(x-5)=0
• Question 8

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

4x2 + 17x - 15 = 0

x = 3/4
x = -5
EDDIE SAYS
(4x-3)(x+5)=0
• Question 9

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

6x2 + 17x - 28 = 0

x = -4
x = 7/6
EDDIE SAYS
(6x-7)(x+4)=0
• Question 10

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

3x2 - 290x - 1000 = 0