GCSE Maths · Higher · Chapter 8: Algebraic manipulation · Lesson 3

Factorising quadratics

Grades 5–7About 50 minutesNo calculator39 marks

Hints online, answers free with an account:
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NameClassDate

Do Now

Grades 4–6

The first question is what today's lesson needs. The others bring back earlier topics.

Grades 5–6

Your teacher works through each example with you. Then try the one beside it.

Example 1

Factorise $x^{2} - x - 56$ .

Hint Two numbers that multiply to

- 56

and add to

- 1

. One of them is negative.

Example 2

Factorise $3 x^{2} - x - 10$ .

Hint Multiply

3 \times (- 10) = - 30

. Find two numbers that multiply to

- 30

and add to

- 1

, then split the middle term.

Grades 5–6

C1
Factorise $x^{2} - 18 x + 77$ .
[2 marks]
Answer
C2
Solve $x^{2} - 6 x - 55 = 0$ by factorising.
[2 marks]
Answer $x = \dots\dots$ or $x = \dots\dots$

C3
Factorise fully $5 x^{2} - 20 x - 60$ .
[2 marks]
Answer
C4
Factorise $9 x^{2} - 49$ .
[2 marks]
Answer
C5
Factorise $16 a^{2} - 81 b^{2}$ .
[2 marks]
Answer
C6
Factorise $x^{2} + 5 x y - 24 y^{2}$ .
[2 marks]
Answer
C7
$x^{2} + b x + 18$ factorises into two brackets with whole numbers in them. $b$ is a positive whole number. Write down every possible value of $b$ .
[2 marks]
Answer

Grades 6–7

D1
Ana says, " $x^{2} + 9 x - 36 = (x - 12) (x + 3)$ ."
Show that Ana is wrong, and write the correct factorisation.
[2 marks]

Grade 8 and beyond

No route is given. The hints are at the end of the sheet. Use one at a time.

Colour one circle on each line.

	Not yet	Nearly	Yes
I can factorise $x^{2} + b x + c$ , reading the signs first.
I can factorise a difference of two squares, with one letter or two.
I can factorise $a x^{2} + b x + c$ by splitting the middle term.

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