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Factorising in Pairs (1)

In this worksheet, students factorise quadratic expressions in pairs.

'Factorising in Pairs (1)' worksheet

Key stage:  KS 4

Curriculum topic:  Algebra

Curriculum subtopic:  Simplify/Manipulate Algebraic Expressions/Fractions

Difficulty level:  

down

Worksheet Overview

QUESTION 1 of 10

This is the first stage in learning how to factorise quadratic expressions.

 

Example

Factorise the following quadratic expression in pairs and then fully.

a2 - 2a + 3a - 6

 

Answer

a2 - 2a + 3a - 6

 

Consider the expression in pairs

a2 - 2a + 3a - 6

 

Factorise each pair
a (a - 2) + 3 (a - 2)

 

Combine

(a + 3) (a - 2) 

 

This is the full factorisation

(a + 3) (a - 2)

Factorise the following quadratic expression in pairs and then fully.

 

a2 + 2a + 3a + 6

 

(a + 2) (a + 6)

(a + 1) (a + 6)

(a + 3) (a + 2)

(a + 2) (a + 4)

Factorise the following quadratic expression in pairs and then fully.

 

a2 + 6a + 2a + 12

 

(a + 2) (a + 6)

(a + 1) (a + 6)

(a + 3) (a + 2)

(a + 2) (a + 4)

Factorise the following quadratic expression in pairs and then fully.

 

a2 - 4a + 2a - 8

 

(a - 2) (a + 6)

(a + 1) (a - 6)

(a - 3) (a - 2)

(a + 2) (a - 4)

Factorise the following quadratic expression in pairs and then fully.

 

a2 - 6a + a - 6

 

(a - 2) (a + 6)

(a + 1) (a - 6)

(a - 3) (a - 2)

(a + 2) (a - 4)

Factorise the following quadratic expression in pairs and then fully.

 

a2 + 6a - 2a - 12

 

(a - 2) (a + 6)

(a + 1) (a - 6)

(a - 3) (a - 2)

(a + 2) (a - 4)

Factorise the following quadratic expression in pairs and then fully.

 

a2 + 3a - 2a - 6

 

(a - 2) (a + 3)

(a + 2) (a - 6)

(a - 3) (a - 2)

(a + 3) (a - 4)

Factorise the following quadratic expression in pairs and then fully.

 

a2 - 2a - 3a + 6

 

(a - 2) (a + 3)

(a + 2) (a - 6)

(a - 3) (a - 2)

(a + 3) (a - 4)

Factorise the following quadratic expression in pairs and then fully.

 

a2 - 4a + 3a - 12

 

(a - 3) (a + 4)

(a + 2) (a - 6)

(a - 6) (a - 2)

(a + 3) (a - 4)

Factorise the following quadratic expression in pairs and then fully.

 

a2 + 4a - 3a - 12

 

(a - 3) (a + 4)

(a + 2) (a - 6)

(a - 6) (a - 2)

(a + 3) (a - 4)

Factorise the following quadratic expression in pairs and then fully.

 

a2 - 9a + 2a - 18

 

(a - 2) (a + 9)

(a + 2) (a - 9)

(a - 6) (a - 3)

(a + 3) (a - 6)

  • Question 1

Factorise the following quadratic expression in pairs and then fully.

 

a2 + 2a + 3a + 6

 

CORRECT ANSWER
(a + 3) (a + 2)
  • Question 2

Factorise the following quadratic expression in pairs and then fully.

 

a2 + 6a + 2a + 12

 

CORRECT ANSWER
(a + 2) (a + 6)
  • Question 3

Factorise the following quadratic expression in pairs and then fully.

 

a2 - 4a + 2a - 8

 

CORRECT ANSWER
(a + 2) (a - 4)
  • Question 4

Factorise the following quadratic expression in pairs and then fully.

 

a2 - 6a + a - 6

 

CORRECT ANSWER
(a + 1) (a - 6)
  • Question 5

Factorise the following quadratic expression in pairs and then fully.

 

a2 + 6a - 2a - 12

 

CORRECT ANSWER
(a - 2) (a + 6)
  • Question 6

Factorise the following quadratic expression in pairs and then fully.

 

a2 + 3a - 2a - 6

 

CORRECT ANSWER
(a - 2) (a + 3)
  • Question 7

Factorise the following quadratic expression in pairs and then fully.

 

a2 - 2a - 3a + 6

 

CORRECT ANSWER
(a - 3) (a - 2)
  • Question 8

Factorise the following quadratic expression in pairs and then fully.

 

a2 - 4a + 3a - 12

 

CORRECT ANSWER
(a + 3) (a - 4)
  • Question 9

Factorise the following quadratic expression in pairs and then fully.

 

a2 + 4a - 3a - 12

 

CORRECT ANSWER
(a - 3) (a + 4)
  • Question 10

Factorise the following quadratic expression in pairs and then fully.

 

a2 - 9a + 2a - 18

 

CORRECT ANSWER
(a + 2) (a - 9)
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