Are harder quadratics on the Foundation paper?

No. Foundation tier stops at x^2 + bx + c and the difference of two squares. Factorising ax^2 + bx + c when a is bigger than 1 sits in the Higher-only part of spec reference A4, so it appears on 1MA1 Higher papers only.

What does 'factorise fully' mean on Edexcel papers?

It means take out every common factor and then keep going if what is left factorises again. For 2x^2 - 18 the full answer is 2(x + 3)(x - 3); stopping at 2(x^2 - 9) usually scores one of the two marks. The word 'fully' is a signal that there is more than one step.

How many marks is factorising worth on Edexcel GCSE Higher?

A standalone question is normally 1-2 marks: one mark for a common factor, two for a quadratic. It is worth more than that in practice because factorising is the first step in solving quadratics, simplifying algebraic fractions and handling quadratic inequalities, and losing it costs the marks that follow.

Can I use a calculator to factorise in the exam?

On Papers 2 and 3 you can solve the quadratic on a calculator and work backwards to the brackets, though you still have to write the brackets down. Paper 1 is non-calculator, so practise listing factor pairs by hand. Whichever paper you are on, expand your answer to check it.

Factorising - Edexcel GCSE Higher Maths

Typically 2-4 marks per paper, plus marks in questions that depend on it · Spec 1MA1

Factorising is writing an expression as a product, which is the reverse of expanding brackets. Edexcel's 1MA1 spec reference A4 covers three versions of it: taking out a common factor (a number, a letter, or both), factorising $x^2 + bx + c$ into two brackets including the difference of two squares, and factorising $ax^2 + bx + c$ where $a$ is bigger than 1. That last one is Higher tier only, so a Foundation candidate never meets $3x^2 + 10x + 8$ .

Standalone factorising questions usually sit in the first third of a paper for 1-2 marks, often worded 'Factorise fully'. The bigger returns come later, when factorising is step one of something longer: solving a quadratic, simplifying an algebraic fraction such as $\frac{x^2 - 25}{x + 5}$ , or turning a quadratic inequality into critical values. It can be set on any of the three papers, and Paper 1 has no calculator, so you cannot solve the quadratic first and read the brackets off the roots. The factor pair has to be found by listing.

Two marks is the usual allocation for a quadratic, and one of them is normally available for brackets that expand to give two of the three terms correctly, so a single sign slip still scores something. The word 'fully' is what catches people out: $2(x^2 - 9)$ is a factorisation of $2x^2 - 18$ , but it is not the full one, and the mark scheme wants $2(x + 3)(x - 3)$ . Expanding your brackets back takes about ten seconds and catches nearly every error in this topic.

Worked example

(a) Factorise

2x^2 + 9x + 4

(b) Hence solve

2x^2 + 9x + 4 = 0

[4 marks]

Multiply the coefficient of $x^2$ by the constant: $2 \times 4 = 8$ . Now find two numbers with product 8 and sum 9. They are 8 and 1.
M1: a correct pair from the product $ac$ and the sum $b$
Split the middle term and group: $2x^2 + 8x + x + 4 = 2x(x + 4) + 1(x + 4) = (2x + 1)(x + 4)$ .
A1: fully correct brackets; expanding back returns $2x^2 + 9x + 4$
For part (b), a product is zero only when a factor is zero, so $2x + 1 = 0$ or $x + 4 = 0$ .
M1: using the factorised form from part (a) rather than starting again
Solve each bracket: $x = -\frac{1}{2}$ and $x = -4$ .
A1: both solutions stated, including the fractional one

Practice questions

These are original questions in Edexcel 1MA1 Higher style. Many ask for the numbers inside the brackets rather than the brackets themselves, so typing stays simple: for $(x + a)(x + b)$ you enter $a$ and $b$ , and the stem always says which is which. Work them without a calculator, since Paper 1 gives you no choice, and expand your brackets back before you submit.

No account needed: the questions below are always free to check, plus 8 extra questions today. Your score so far updates as you go.

Question 1 Exam pace [2 marks]

$x^2 + 3x - 28$ factorises to $(x + p)(x - q)$ , where $p$ and $q$ are positive integers. Find $p$ and $q$ .

p = q =
Question 2 Exam pace [3 marks]

Solve $x^2 + 7x + 10 = 0$ by factorising. Give both solutions.

larger x = smaller x =
Question 3 Exam pace [2 marks]

Use the difference of two squares to work out $83^2 - 17^2$ without a calculator.

Your answer (fractions like 1/2 are fine)
Question 4 Exam pace [1 mark]

A student writes $8x^2 - 12x = 2(4x^2 - 6x)$ . Which of these is the fully factorised form?

Answer options for question 4
$4x(2x - 3)$ $2x(4x - 6)$ $4(2x^2 - 3x)$ $2(4x^2 - 6x)$
Question 5 Stretch [3 marks]

Factorising $5x^3 - 45x$ fully gives $kx(x + a)(x - a)$ , where $k$ and $a$ are positive integers. Find $k$ and $a$ .

k = a =
Question 6 Stretch [2 marks]

Factorise $4x^2 + 8x + 3$ .

Answer options for question 6
$(2x + 1)(2x + 3)$ $(4x + 1)(x + 3)$ $(4x + 3)(x + 1)$ $(2x + 3)^2$

Common mistakes examiners see

Taking out part of the common factor rather than all of it, for example writing $12x^2 - 18x = 2(6x^2 - 9x)$ or $3(4x^2 - 6x)$ instead of $6x(2x - 3)$ .

After you write the bracket, read it back and ask whether the terms inside still share anything. If they do, you have not answered 'factorise fully' and the second mark is gone.
Factorising only the first two terms of a three-term quadratic, so $6x^2 - 5x - 4$ is handed in as $x(6x - 5) - 4$ .

A factorised answer is a product with nothing added or subtracted outside it. If your final line still has a loose $+$ or $-$ at the end, it is not factorised.
Applying the difference of two squares to a sum, giving $x^2 + 25 = (x + 5)(x - 5)$ .

Expand $(x + 5)(x - 5)$ : the middle terms cancel and you get $x^2 - 25$ . A sum of two squares does not factorise, so leave it alone.
Not square rooting the coefficient, so $9x^2 - 25$ becomes $(9x + 5)(9x - 5)$ , which expands to $81x^2 - 25$ .

Square root the whole term, coefficient included: $\sqrt{9x^2} = 3x$ and $\sqrt{25} = 5$ , giving $(3x + 5)(3x - 5)$ .
Pairing the right numbers with the wrong signs, writing $x^2 - 2x - 15 = (x - 3)(x + 5)$ when the brackets expand to $x^2 + 2x - 15$ .

Check the sum as well as the product before you commit: you need two numbers multiplying to $-15$ and adding to $-2$ , which is $+3$ and $-5$ , so the brackets are $(x + 3)(x - 5)$ .

Frequently asked questions

Are harder quadratics on the Foundation paper?: No. Foundation tier stops at $x^2 + bx + c$ and the difference of two squares. Factorising $ax^2 + bx + c$ when $a$ is bigger than 1 sits in the Higher-only part of spec reference A4, so it appears on 1MA1 Higher papers only.
What does 'factorise fully' mean on Edexcel papers?: It means take out every common factor and then keep going if what is left factorises again. For $2x^2 - 18$ the full answer is $2(x + 3)(x - 3)$ ; stopping at $2(x^2 - 9)$ usually scores one of the two marks. The word 'fully' is a signal that there is more than one step.
How many marks is factorising worth on Edexcel GCSE Higher?: A standalone question is normally 1-2 marks: one mark for a common factor, two for a quadratic. It is worth more than that in practice because factorising is the first step in solving quadratics, simplifying algebraic fractions and handling quadratic inequalities, and losing it costs the marks that follow.
Can I use a calculator to factorise in the exam?: On Papers 2 and 3 you can solve the quadratic on a calculator and work backwards to the brackets, though you still have to write the brackets down. Paper 1 is non-calculator, so practise listing factor pairs by hand. Whichever paper you are on, expand your answer to check it.

Factorising - Edexcel GCSE Higher Maths

Worked example

Practice questions

Common mistakes examiners see

Frequently asked questions

Related topics