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Factorising Trinomial Expressions (2a)

In this worksheet, students factorise simple trinomial expressions.

'Factorising Trinomial Expressions (2a)' worksheet

Key stage:  KS 4

Curriculum topic:  Algebra

Curriculum subtopic:  Simplify/Manipulate Algebraic Expressions/Fractions

Difficulty level:  

down

Worksheet Overview

QUESTION 1 of 10

A trinomial or quadratic expression takes the form ax2 + bx + c where a, b and c are numbers.

In this worksheet, we will only consider cases when a = 1.

Sometimes it is not possible to factorise this expression into two brackets but, when it is, we can follow this method.

In x2 + bx + c  we look for pairs of numbers which multiply to give c and add to give b.

  

Example

Factorise the following quadratic expression.

x2 - 7x + 12

 

Answer

x2 - 7x + 12

 

Here we have b = -7 and c = 12.

So we list the factor pairs of 12 and see which pair adds to give -7.

 

Factor Pairs Sum of factors
   1 and 12 13
   -1 and -12 -13
   2 and 6 8
   -2 and -6 -8
   3 and 4 7
   -3 and -4

-7

 

We now split the middle term -7x using the chosen factor pair i.e. -3x and -4x

x2 - 3x - 4x +12

 

Consider the expression in pairs

x2 - 3x - 4x + 12

 

Factorise each pair

x (x - 3) - 4 (x - 3)

 

Combine

(x - 4) (x - 3) 

 

This is the full factorisation

(x - 4) (x - 3)

Factorise the following quadratic expression.

x2 + 5x - 6

 

(x - 2) (x +4)

(x - 3) (x - 2)

(x + 6) (x - 1)

(x - 2) (x - 6)

Factorise the following quadratic expression.

x2 - 8x + 12

 

(x - 2) (x - 6)

(x - 1) (x - 6)

(x - 3) (x - 2)

(x - 2) (x - 4)

Factorise the following quadratic expression.

x2 + 5x + 6

 

(x - 2) (x + 6)

(x - 1) (x - 8)

(x + 3) (x + 2)

(x + 2) (x - 4)

Factorise the following quadratic expression.

x2 - 2x - 8

 

(x - 2) (x + 4)

(x - 1) (x - 8)

(x - 3) (x + 2)

(x + 2) (x - 4)

Factorise the following quadratic expression.

x2 - 8x - 9

 

(x - 3) (x - 3)

(x + 1) (x - 9)

(x - 2) (x - 8)

(x - 4) (x - 4)

Factorise the following quadratic expression.

x2 + 8x + 16

 

(x - 3) (x + 3)

(x - 1) (x - 9)

(x + 2) (x + 8)

(x + 4) (x + 4)

Factorise the following quadratic expression.

x2 + 6x - 27

 

(x + 3) (x - 3)

(x - 3) (x + 9)

(x - 5) (x - 8)

(x - 3) (x - 9)

Factorise the following quadratic expression.

x2 - 11x + 24

 

(x + 3) (x - 8)

(x - 2) (x - 12)

(x - 3) (x - 8)

(x - 6) (x - 4)

Factorise the following quadratic expression.

x2 - 5x - 36

 

(x + 18) (x - 2)

(x - 12) (x - 3)

(x + 6) (x - 6)

(x - 9) (x + 4)

Factorise the following quadratic expression.

x2 - 16x - 36

 

(x - 18) (x + 2)

(x + 12) (x - 3)

(x - 6) (x - 6)

(x - 9) (x - 4)

  • Question 1

Factorise the following quadratic expression.

x2 + 5x - 6

 

CORRECT ANSWER
(x + 6) (x - 1)
  • Question 2

Factorise the following quadratic expression.

x2 - 8x + 12

 

CORRECT ANSWER
(x - 2) (x - 6)
  • Question 3

Factorise the following quadratic expression.

x2 + 5x + 6

 

CORRECT ANSWER
(x + 3) (x + 2)
  • Question 4

Factorise the following quadratic expression.

x2 - 2x - 8

 

CORRECT ANSWER
(x + 2) (x - 4)
  • Question 5

Factorise the following quadratic expression.

x2 - 8x - 9

 

CORRECT ANSWER
(x + 1) (x - 9)
  • Question 6

Factorise the following quadratic expression.

x2 + 8x + 16

 

CORRECT ANSWER
(x + 4) (x + 4)
  • Question 7

Factorise the following quadratic expression.

x2 + 6x - 27

 

CORRECT ANSWER
(x - 3) (x + 9)
  • Question 8

Factorise the following quadratic expression.

x2 - 11x + 24

 

CORRECT ANSWER
(x - 3) (x - 8)
  • Question 9

Factorise the following quadratic expression.

x2 - 5x - 36

 

CORRECT ANSWER
(x - 9) (x + 4)
  • Question 10

Factorise the following quadratic expression.

x2 - 16x - 36

 

CORRECT ANSWER
(x - 18) (x + 2)
---- OR ----

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