Find the highest common factor: HCF = 2 Divide each term by 2: 2x ÷ 2 = x, 6 ÷ 2 = 3 Write the factorised form: 2(x + 3) Answer: 2(x + 3)

Find the highest common factor: HCF = 3 Divide each term by 3: 3x ÷ 3 = x, 12 ÷ 3 = 4 Write the factorised form: 3(x + 4) Answer: 3(x + 4)

Find the highest common factor: HCF = 5 Divide each term by 5: 5x ÷ 5 = x, 15 ÷ 5 = 3 Write the factorised form: 5(x - 3) Answer: 5(x - 3)

Find the common factor: each term contains x Take out x: x(x + 3) Check by expanding: x(x + 3) Answer: x(x + 3)

Find the common factor: each term contains x Take out x: x(x - 7) Check by expanding: x(x - 7) Answer: x(x - 7)

Factorising quadratics Worked Solutions — GCSE Maths

Fully worked, step-by-step solutions to GCSE Factorising quadratics questions. See exactly how to solve problems on common factor, factorising, factorising quadratics, factor pairs.

common factorfactorisingfactorising quadraticsfactor pairsdifference of two squaresperfect square

GCSE Foundation70 questionsStep-by-step solutions

Question 1

1 markeasy

Factorise

2x + 6

Worked solution

Find the highest common factor
$\text{HCF} = 2$
Every term divides by 2.
Divide each term by 2
$2x \div 2 = x,\quad 6 \div 2 = 3$
Write what is left inside the bracket.
Write the factorised form
$2(x + 3)$
Check: $2 \times x = 2x$ and $2 \times 3 = 6$ , giving $2x + 6$ .

Answer

2(x + 3)

Question 2

1 markeasy

Factorise

3x + 12

Worked solution

Find the highest common factor
$\text{HCF} = 3$
Every term divides by 3.
Divide each term by 3
$3x \div 3 = x,\quad 12 \div 3 = 4$
Write what is left inside the bracket.
Write the factorised form
$3(x + 4)$
Check: $3 \times x = 3x$ and $3 \times 4 = 12$ .

Answer

3(x + 4)

Question 3

1 markeasy

Factorise

5x - 15

Worked solution

Find the highest common factor
$\text{HCF} = 5$
Every term divides by 5.
Divide each term by 5
$5x \div 5 = x,\quad 15 \div 5 = 3$
Write what is left inside the bracket.
Write the factorised form
$5(x - 3)$
Check: 5 $\times$ $x = 5x$ and 5 $\times$ $(-3) = -15$ .

Answer

5(x - 3)

Question 4

1 markeasy

Factorise

x^2 + 3x

Worked solution

Find the common factor
$\text{each term contains } x$
Both terms have a factor of x.
Take out x
$x(x + 3)$
Divide each term by x and write x outside.
Check by expanding
$x(x + 3)$
Check: x $\times$ $x = x^2$ and x $\times$ $3 = 3x$ .

Answer

x(x + 3)

Question 5

1 markeasy

Factorise

x^2 - 7x

Worked solution

Find the common factor
$\text{each term contains } x$
Both terms have a factor of x.
Take out x
$x(x - 7)$
Divide each term by x and write x outside.
Check by expanding
$x(x - 7)$
Check: x $\times$ $x = x^2$ and x $\times$ $(-7) = -7x$ .

Answer

x(x - 7)

Unlock 65 more Factorising quadratics questions

Create a free account to work through every GCSE Factorising quadratics question with instant step-by-step worked solutions, progress tracking and interactive lessons.

Full worked solutions for every question
Interactive lessons and instant feedback
Track your mastery across every topic

Create a Free Account

No card required · Free forever

More Factorising quadratics practice

Hard Questions Practice Questions

Factorising quadratics Worked Solutions — GCSE Maths

Worked solution

Worked solution

Worked solution

Worked solution

Worked solution

Unlock 65 more Factorising quadratics questions

More Factorising quadratics practice

Related Algebra topics