Class 8 · Maths · 2026-27

Factorisation with Answers

Most children who are stuck on factorisation are not unable to factorise - they are guessing which method to try. There are four, and they go in a fixed order: common factor, identity, grouping, splitting the middle term. A child working down that list rarely gets stuck; a child starting anywhere gets stuck constantly.

34 questions · 30 minutes · full answer key · free printable PDF · no sign-up

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Factorisation

Class 8 Maths · Factorisation · 34 questions with answers

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Most children who are stuck on factorisation are not unable to factorise - they are guessing which method to try. There are four, and they go in a fixed order: common factor, identity, grouping, splitting the middle term. A child working down that list rarely gets stuck; a child starting anywhere gets stuck constantly.

Takes out the highest common factor before anything else
Recognises a difference of squares and a perfect square trinomial
Factorises a four-term expression by grouping
Splits the middle term of a quadratic, including when the leading coefficient is not 1
Chooses the method in the right order rather than by trial

Exercise 1 of 3 · 10 questions

Factorise by taking out the common factor.

Write the answer · Warm-up

Here’s one done for you

12a²b - 18ab² = 6ab(2a - 3b). Two things to check every time: the number factor is the highest common one (6, not 2 or 3), and the letters are taken to the lowest power that appears in both (ab, not a²b). Taking out a partial factor is not wrong exactly, but it leaves work behind and loses marks that were already earned.

1)6x + 9
2)12a²b - 18ab²
3)5x² + 10x
4)7pq + 14p
5)4m³ - 8m²
6)8x + 20
7)15a²b - 25ab²
8)6x² + 9x
9)3m³ - 12m²
10)9pq + 12p

Answers

1) 3(2x + 3).
2) 6ab(2a - 3b). The common factor is 6ab - take the highest one, not just any one.
3) 5x(x + 2).
4) 7p(q + 2).
5) 4m²(m - 2).
6) 4(2x + 5)
7) 5ab(3a - 5b)
8) 3x(2x + 3)
9) 3m²(m - 4)
10) 3p(3q + 4)

Exercise 2 of 3 · 12 questions

Factorise using an identity, or by grouping.

Write the answer · Guided

Here’s one done for you

ax + ay + bx + by = (a + b)(x + y). Grouping works when there are four terms and no factor common to all of them. Take a from the first pair and b from the second: a(x + y) + b(x + y). Both now share (x + y), so it comes out. If the second bracket does not match the first, try pairing the terms differently before deciding grouping will not work.

1)x² - 16
2)9a² - 25
3)x² + 10x + 25
4)4y² - 12y + 9
5)ax + ay + bx + by
6)x² + 3x + 2x + 6
7)x² - 49
8)16a² - 81
9)x² + 14x + 49
10)9y² - 24y + 16
11)px + py + qx + qy
12)x² + 5x + 3x + 15

Answers

1) (x + 4)(x - 4). Difference of squares.
2) (3a + 5)(3a - 5). Since 9a² = (3a)².
3) (x + 5)². A perfect square, because 25 = 5² and 10x = 2 × x × 5.
4) (2y - 3)². Since 4y² = (2y)², 9 = 3² and 12y = 2 × 2y × 3.
5) (a + b)(x + y). Group as a(x + y) + b(x + y).
6) (x + 3)(x + 2). Group as x(x + 3) + 2(x + 3).
7) (x + 7)(x - 7)
8) (4a + 9)(4a - 9)
9) (x + 7)²
10) (3y - 4)²
11) (x + y)(p + q)
12) (x + 3)(x + 5)

Exercise 3 of 3 · 12 questions

Factorise by splitting the middle term.

Write the answer · Practice

Here’s one done for you

2x² + 7x + 3 = (2x + 1)(x + 3). When the number in front of x² is not 1, the two numbers must multiply to the first coefficient times the last - here 2 × 3 = 6 - and add to the middle one, 7. That gives 6 and 1, so write 2x² + 6x + x + 3 and group: 2x(x + 3) + 1(x + 3). Children who learn the shortcut for x² + bx + c and are never shown this extension get stuck on every question where the leading coefficient is not 1.

1)x² + 7x + 12
2)x² - 5x + 6
3)x² + x - 12
4)x² - 2x - 15
5)2x² + 7x + 3
6)3x² - 10x + 8
7)x² + 11x + 30
8)x² - x - 20
9)x² - 9x + 20
10)x² + 2x - 24
11)2x² + 9x + 4
12)3x² + 11x + 6

Answers

1) (x + 3)(x + 4). Two numbers multiplying to 12 and adding to 7.
2) (x - 2)(x - 3). Product 6, sum -5, so both are negative.
3) (x + 4)(x - 3). Product -12, sum +1.
4) (x - 5)(x + 3). Product -15, sum -2.
5) (2x + 1)(x + 3). Product 2 × 3 = 6, sum 7, so split as 6x + x: 2x² + 6x + x + 3.
6) (3x - 4)(x - 2). Product 3 × 8 = 24, sum -10, so split as -6x - 4x.
7) (x + 5)(x + 6)
8) (x - 5)(x + 4)
9) (x - 4)(x - 5)
10) (x + 6)(x - 4)
11) (2x + 1)(x + 4)
12) (3x + 2)(x + 3)

While your child works

Ask 'which method, and why that one?' before any factorising happens. Common factor, identity, grouping, middle term - in that order.
Check the answer by expanding it back. It takes fifteen seconds and catches every error.
When the number in front of x² is not 1, the product to aim for is first coefficient times last. That extension is the one most often never taught.

Before you print it

What is on this worksheet

3 exercises, 34 questions, about 30 minutes. Every exercise has an answer key, printed on its own page so it can be kept back. 3 exercises start with a question already worked out, so you can check the method before helping.

Exercise	What the child does	Questions	Worked example
1	Written answers	10	Yes
2	Written answers	12	Yes
3	Written answers	12	Yes

More Class 8 Maths worksheets

Each one is a complete sheet with its own answer key, free to print.

Questions parents ask

About this worksheet

In what order should factorisation methods be tried?

Common factor first, then an identity, then grouping, then splitting the middle term. Most children who are stuck are guessing which to use rather than unable to use any of them.

Why does my child get stuck when the number in front of x² is not 1?

Because the shortcut they learned only works when it is 1. With 2x² + 7x + 3 the two numbers must multiply to 2 × 3 = 6 and add to 7 - and that extension is very often never taught.

Does this Class 8 Maths worksheet come with answers?

Yes. Every exercise has a full answer key, and it prints on its own page at the end rather than beside the questions - so you can hand your child the sheet and keep the answers back. Some exercises also show one question already worked out, with the method rather than just the result, which is the part most answer keys leave out.

Is there a free printable PDF?

Yes, and there is no sign-up, no email and no account. The download button at the top of the sheet gives you the whole thing - all 34 questions across 3 exercises, plus the answer key - laid out to print on A4.

How long does this worksheet take?

About 30 minutes for 34 questions, though that is a guide rather than a target. It is designed to be split: the exercises are ordered so stopping halfway still leaves a complete piece of work, which matters more than finishing at this age.

Can I use it if my child is in a different class?

Often, yes - these topics are taught across several years and schools vary in when they arrive. Judge by the questions rather than the class on the label. If the first exercise is a struggle the level below is the better start, and the same topic at other levels is linked further up this page.

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