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Factorising Trinomial Expressions (1)

In this worksheet, students factorise trinomial expressions.

'Factorising Trinomial Expressions (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

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

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

In ax2 + bx + c  we look for pairs of numbers which multiply to give ac and add to give b.

  

Example

Factorise the following quadratic expression.

3x2 - 2x - 8

 

Answer

3x2 - 2x - 8

 

Here we have a = 3, b = -2 and c = -8.

So we list the factor pairs of -24 and see which pair adds to give -2.

 

Factor Pairs Sum of factors
   1 and -24 -23
   -1 and 24 23
   2 and -12 -10
   -2 and 12 10
   3 and -8 -5
   -3 and 8

5

  4 and -6 -2
   -4 and 6 2

 

We now split the middle term -2x using the chosen factor pair i.e. 4x and -6x

3x2 + 4x - 6x - 8

 

Consider the expression in pairs

3x2 + 4x - 6x - 8

 

Factorise each pair

x (3x + 4) - 2 (3x + 4)

 

Combine

(x - 2) (3x + 4) 

 

This is the full factorisation

(x - 2) (3x + 4)

Factorise the following quadratic expression.

 

2x2 + 11x + 15

(x - 3) (x + 5)

(x + 5) (x + 3)

(x + 3) (2x + 5)

(2x + 3) (x + 5)

Factorise the following quadratic expression.

 

2x2 + 13x + 15

(x - 3) (x + 5)

(x + 5) (x + 3)

(x + 3) (2x + 5)

(2x + 3) (x + 5)

Factorise the following quadratic expression.

 

2x2 + 17x + 35

(2x - 5) (x + 7)

(2x + 7) (x + 5)

(x + 7) (2x + 5)

(2x + 35) (x + 1)

Factorise the following quadratic expression.

 

2x2 + 37x + 35

(2x - 5) (x + 7)

(2x + 7) (x + 5)

(x + 7) (2x + 5)

(2x + 35) (x + 1)

Factorise the following quadratic expression.

 

2x2 + 9x - 35

(2x - 5) (x + 7)

(2x - 7) (x + 5)

(x - 7) (2x + 5)

(2x + 35) (x + 1)

Factorise the following quadratic expression.

 

2x2 - 9x - 35

(2x - 5) (x + 7)

(2x - 7) (x + 5)

(x - 7) (2x + 5)

(2x + 35) (x + 1)

Factorise the following quadratic expression.

 

4x2 + 3x - 10

(4x - 5) (x + 2)

(4x + 1) (x - 10)

(x - 2) (4x + 5)

(4x - 1) (x + 10)

Factorise the following quadratic expression.

 

4x2 + 39x - 10

(4x - 5) (x + 2)

(4x + 1) (x - 10)

(x - 2) (4x + 5)

(4x - 1) (x + 10)

Factorise the following quadratic expression.

 

6x2 - 19x + 14

(6x - 7) (x - 2)

(6x - 1) (x - 14)

(x - 2) (6x + 7)

(6x - 2) (x - 7)

Factorise the following quadratic expression.

 

6x2 - 23x + 15

(6x + 5) (x - 3)

(6x - 1) (x - 15)

(x - 1) (6x + 5)

(6x - 5) (x - 3)

  • Question 1

Factorise the following quadratic expression.

 

2x2 + 11x + 15

CORRECT ANSWER
(x + 3) (2x + 5)
EDDIE SAYS
We look for factor pairs that multiply to give 30 and add to give 11.
These are 5 and 6.
Factorise 2x² + 5x + 6x + 15 in pairs.
  • Question 2

Factorise the following quadratic expression.

 

2x2 + 13x + 15

CORRECT ANSWER
(2x + 3) (x + 5)
EDDIE SAYS
We look for factor pairs that multiply to give 30 and add to give 13.
These are 10 and 3.
Factorise 2x² + 10x + 3x + 15 in pairs.
  • Question 3

Factorise the following quadratic expression.

 

2x2 + 17x + 35

CORRECT ANSWER
(2x + 7) (x + 5)
EDDIE SAYS
We look for factor pairs that multiply to give 70 and add to give 17.
These are 10 and 7.
Factorise 2x² + 10x + 7x + 35 in pairs.
  • Question 4

Factorise the following quadratic expression.

 

2x2 + 37x + 35

CORRECT ANSWER
(2x + 35) (x + 1)
EDDIE SAYS
We look for factor pairs that multiply to give 70 and add to give 37.
These are 2 and 35.
Factorise 2x² + 2x + 35x + 35 in pairs.
  • Question 5

Factorise the following quadratic expression.

 

2x2 + 9x - 35

CORRECT ANSWER
(2x - 5) (x + 7)
EDDIE SAYS
We look for factor pairs that multiply to give -70 and add to give 9.
These are 14 and -5.
Factorise 2x² + 14x - 5x - 35 in pairs.
  • Question 6

Factorise the following quadratic expression.

 

2x2 - 9x - 35

CORRECT ANSWER
(x - 7) (2x + 5)
EDDIE SAYS
We look for factor pairs that multiply to give -70 and add to give -9.
These are 5 and -14.
Factorise 2x² + 5x - 14x - 35 in pairs.
  • Question 7

Factorise the following quadratic expression.

 

4x2 + 3x - 10

CORRECT ANSWER
(4x - 5) (x + 2)
EDDIE SAYS
We look for factor pairs that multiply to give -40 and add to give +3.
These are 8 and -5.
Factorise 4x² + 8x - 5x - 10 in pairs.
  • Question 8

Factorise the following quadratic expression.

 

4x2 + 39x - 10

CORRECT ANSWER
(4x - 1) (x + 10)
EDDIE SAYS
We look for factor pairs that multiply to give -40 and add to give +39.
These are 40 and -1.
Factorise 4x² + 40x - x - 10 in pairs.
  • Question 9

Factorise the following quadratic expression.

 

6x2 - 19x + 14

CORRECT ANSWER
(6x - 7) (x - 2)
EDDIE SAYS
We look for factor pairs that multiply to give 84 and add to give -19.
These are -12 and -7.
Factorise 6x² - 12x - 7x + 14 in pairs.
  • Question 10

Factorise the following quadratic expression.

 

6x2 - 23x + 15

CORRECT ANSWER
(6x - 5) (x - 3)
EDDIE SAYS
We look for factor pairs that multiply to give 90 and add to give -23.
These are -18 and -5.
Factorise 6x² - 18x - 5x + 15 in pairs.
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