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.

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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)

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