Middle Years

2.05 Factorising

Worksheet
Factors
1

State whether the following are factors of 33 wy:

a
11
b
66 w y
c
yw
d
3w
e
y w^{2}
f
33
2

Find the highest common factor of the following groups of numbers:

a

2 and 6 x

b

3 and 15x

c

6x and 21

d

10 and 16 u

e

35 x and 14

f

4x and 16xy

g

15 and 5 x

h

24 m, 12 n and 18 q

i

27 m, 24 n and 15 q

Factorisation
3

Complete the factorisation of the following expressions:

a

2 a + 16 = ⬚ \left(a + 8\right)

b

5 y - 30 = ⬚ \left(y - 6\right)

c

24 n + 15 = ⬚ \left( 8 n + 5\right)

d

16 a - 6 = ⬚ \left( 8 a - 3\right)

e

6 v + 18 = 6 \left(⬚\right)

f

9 a - 36 = 9 \left(⬚\right)

g

24 a + 9 = 3 \left(⬚\right)

h

6 w - 27 = 3 \left(⬚\right)

i

4 r + 12 = ⬚ \left(r + 3\right)

j

5 v - 30 = ⬚ \left(v - 6\right)

k

18 c - 24 = ⬚ \left( 3 c - 4\right)

l

2 r + 14 = 2 \left(⬚\right)

m

5 t - 10 = 5 \left(⬚\right)

n

54 u + 12 = 6 \left(⬚\right)

4

Factorise the following expressions:

a

6 v + 30

b

6 a - 48

c

45 t - 40

d

2 m + 10 n

e

54 - 60 f g

f

8 g - 72 h

g

9 f + 15 g

h

3 w + 15

i

2 c - 18

j

40 c - 35

k

6 w + 30 y

l

14 y + 4 w

m

4 a - 14 b

n

32 - 36 j k

o

8 j k t - 18

p

3 f g - 10 f h

q

3 r t w - 8 r w

r

4 r t - 6 r^{2} t

s

16wy-36w^2y

5

Complete the following factorisation:

2 w - 10 z + 8 y = 2 \left(⬚ - ⬚ + ⬚\right)

6

Factorise the following completely:

a

8 g + 28 h - 20

b

4 w + 4 z + 4 y

c

4 u - 12 v + 20 w

d

10 m - 25 n - 15 p

e

3 m - 6 n + 12 p

f

10 g - 35 h + 15

g

z w - z y - z k

h

60 r - 25 r t - 35 r^{2} t

i

12m-32mn-20m^2n

j

16z-32yz-24y^2z

k

25 r^2t - 15 r t^2 - 45 r^{2} t^2

Factorisation of negatives
7

Factor out the negative coefficient of the following expressions:

a

- 4 r - 3 s

b

- 7 r - 7 s

c

- 2 - 9 r

d

- 8x - 5y

8

Factorise the following expressions:

a

- 8 b - 16

b

- 18 a + 16

c

- 80 v - 30

d

- 36 - 6 x

e

- 25 u - 35 v

f

- 35 m + 49 n

g

- 8 p q r - 6 p r

h

- 8 w^{2} + 3 w^{2} y

i

- 24 j^{2} - 27 j^{2} k

j

- 8 m^{2} + 9 m n

k

-10u^2v+9uv^2

l

-21j^2-36j^2k

m

- 2 s - 10

n

- 8 v^{2} + 56

o

- 12 s + 10

p

- 28 b - 21

q

- 63 r^{2} + 28

r

- 4 m - 32 n

s

- 49 y - 21 w

9

Factorise the following completely:

a

- 18 p - 9 q - 45 r

b

- 10 r - 25 s + 20 t

c

- 20 u - 25 v + 45 w

d

- 8 w - 18 y - 10 z