 # Factorising Trinomial Expressions (2)

In this worksheet, students factorise trinomial expressions. Key stage:  KS 4

Curriculum topic:  Algebra

Curriculum subtopic:  Simplify/Manipulate Algebraic Expressions/Fractions

Difficulty level:   ### 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.

18x2 + 3x - 10

18x2 + 3x - 10

Here we have a = 18, b = 3 and c = -10.

So we list the factor pairs of -180 and see which pair adds to give 3.

The first two factor pairs below are too wildly out, so, rather than looking at the extreme factor pairs, we concentrate on ones that are closer together.

Factor Pairs Sum of factors
1 and -180 -179
-1 and 180 179
18 and -10 8
-18 and 10 -8
15 and -12 3
-15 and 12

-3

30 and -6 24
-30 and 6 -24

We now split the middle term +3x using the chosen factor pair i.e. 15x and -12x

18x2 + 15x - 12x - 10

Consider the expression in pairs

18x2 + 15x - 12x - 10

Factorise each pair

3x (6x + 5) - 2 (6x + 5)

Combine

(3x - 2) (6x + 5)

This is the full factorisation

(3x - 2) (6x + 5)

Factorise the following quadratic expression.

8x2 + 26x + 15

(8x - 3) (x + 5)

(x + 5) (8x + 3)

(4x + 3) (2x + 5)

(2x + 3) (4x + 5)

Factorise the following quadratic expression.

6x2 + 31x + 35

(2x - 5) (3x + 7)

(2x + 7) (3x + 5)

(3x + 7) (2x + 5)

(2x + 35) (3x + 1)

Factorise the following quadratic expression.

4x2 + 72x + 35

(4x - 5) (x + 7)

(2x + 7) (2x + 5)

(2x + 7) (2x + 5)

(2x + 35) (2x + 1)

Factorise the following quadratic expression.

6x2 - x - 35

(6x + 35) (x + 1)

(x - 7) (6x + 5)

(2x - 7) (3x + 5)

(2x - 5) (3x + 7)

Factorise the following quadratic expression.

8x2 + 6x - 35

(2x + 35) (2x + 1)

(4x - 7) (2x + 5)

(2x - 7) (2x + 5)

(4x - 5) (x + 7)

Factorise the following quadratic expression.

8x2 - 11x - 10

(8x - 1) (x + 10)

(x - 2) (8x + 5)

(4x + 1) (2x - 10)

(4x - 5) (2x + 2)

Factorise the following quadratic expression.

12x2 - 23x + 10

(6x - 1) (2x + 10)

(3x - 2) (4x + 5)

(4x + 1) (3x - 10)

(4x - 5) (3x - 2)

Factorise the following quadratic expression.

10x2 + 53x + 15

(10x - 3) (x + 5)

(x + 5) (10x + 3)

(5x + 3) (2x + 5)

(2x + 3) (5x + 5)

Factorise the following quadratic expression.

18x2 - 33x + 14

(9x - 2) (2x - 7)

(9x - 2) (2x + 7)

(6x - 1) (3x - 14)

(6x - 7) (3x - 2)

Factorise the following quadratic expression.

18x2 - 87x + 14

(6x - 2) (3x - 7)

(3x - 2) (6x + 7)

(6x - 1) (3x - 14)

(2x - 7) (9x - 2)

• Question 1

Factorise the following quadratic expression.

8x2 + 26x + 15

(4x + 3) (2x + 5)
EDDIE SAYS
We look for factor pairs that multiply to give 120 and add to give 26.
These are 20 and 6.
Factorise 8x² + 20x + 6x + 15 in pairs.
• Question 2

Factorise the following quadratic expression.

6x2 + 31x + 35

(2x + 7) (3x + 5)
EDDIE SAYS
We look for factor pairs that multiply to give 210 and add to give 31.
These are 10 and 21.
Factorise 6x² + 10x + 21x + 35 in pairs.
• Question 3

Factorise the following quadratic expression.

4x2 + 72x + 35

(2x + 35) (2x + 1)
EDDIE SAYS
We look for factor pairs that multiply to give 140 and add to give 72.
These are 2 and 70.
Factorise 4x² + 2x + 70x + 35 in pairs.
• Question 4

Factorise the following quadratic expression.

6x2 - x - 35

(2x - 5) (3x + 7)
EDDIE SAYS
We look for factor pairs that multiply to give -210 and add to give -1.
These are 14 and -15.
Factorise 6x² + 14x - 15x - 35 in pairs.
• Question 5

Factorise the following quadratic expression.

8x2 + 6x - 35

(4x - 7) (2x + 5)
EDDIE SAYS
We look for factor pairs that multiply to give -280 and add to give 6.
These are 20 and -14.
Factorise 8x² + 20x - 14x - 35 in pairs.
• Question 6

Factorise the following quadratic expression.

8x2 - 11x - 10

(x - 2) (8x + 5)
EDDIE SAYS
We look for factor pairs that multiply to give -80 and add to give -11.
These are 5 and -16.
Factorise 8x² + 5x - 16x - 10 in pairs.
• Question 7

Factorise the following quadratic expression.

12x2 - 23x + 10

(4x - 5) (3x - 2)
EDDIE SAYS
We look for factor pairs that multiply to give 120 and add to give -23.
These are -8 and -15.
Factorise 12x² - 8x - 15x + 10 in pairs.
• Question 8

Factorise the following quadratic expression.

10x2 + 53x + 15

(x + 5) (10x + 3)
EDDIE SAYS
We look for factor pairs that multiply to give 150 and add to give 53.
These are 3 and 50.
Factorise 10x² + 3x + 50x + 15 in pairs.
• Question 9

Factorise the following quadratic expression.

18x2 - 33x + 14

(6x - 7) (3x - 2)
EDDIE SAYS
We look for factor pairs that multiply to give 252 and add to give -33.
These are -12 and -21.
Factorise 18x² - 12x - 21x + 14 in pairs.
• Question 10

Factorise the following quadratic expression.

18x2 - 87x + 14

(6x - 1) (3x - 14)
EDDIE SAYS
We look for factor pairs that multiply to give 252 and add to give -87.
These are -84 and -3.
Factorise 18x² - 84x - 3x + 14 in pairs.
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