Cambridge International Mathematics

Algebra (Expansion and factorisation) (Chapter 1) 41

Example 15 Self Tutor

Find the highest common factor of:

a 8 aand 12 b b 4 x^2 and 6 xy

a 8 a= 2 £ 2 £ 2 £a

12 b= 2 £ 2 £ 3 £b

) HCF=2£ 2

=4

b 4 x^2 = 2 £ 2 £x£x

6 xy= 2 £ 3 £x£y

) HCF=2£x

=2x

Example 16 Self Tutor

Find the HCF of 3(x+3) and (x+ 3)(x+1):

3(x+3)=3£(x+3) (x+ 3)(x+1)=(x+3)£(x+1)

) HCF=(x+3)

EXERCISE 1F

1 Find the missing factor:

a 3 £¤=6a b 3 £¤=15b c 2 £¤=8xy

d 2 x£¤=8x^2 e ¤£ 2 x=2x^2 f ¤£ 5 x=¡ 10 x^2

g ¡a£¤=ab h ¤£a^2 =4a^3 i 3 x£¤=¡ 9 x^2 y

2 Find the highest common factor of the following:

a 2 aand 6 b 5 cand 8 c c 8 rand 27

d 12 kand 7 k e 3 aand 12 a f 5 xand 15 x

g 25 xand 10 x h 24 yand 32 y i 36 band 54 d

3 Find the HCF of the following:

a 23 aband 7 ab b abcand 6 abc c 36 aand 12 ab

d a^2 anda e 9 randr^3 f 3 qandqr

g 3 b^2 and 9 b h dp^2 andpd i 4 rand 8 r^2

j 3 pqand 6 pq^2 k 2 a^2 band 6 ab l 6 xyand 18 x^2 y^2

m 15 a, 20 aband 30 b n 12 wxz, 12 wz, 24 wxyz o 24 p^2 qr, 36 pqr^2

4 Find the HCF of:

a 5(x+2) and (x+ 8)(x+2) b 2(x+5)^2 and 6(x+ 9)(x+5)

c 3 x(x+4) and x^2 (x+2) d 6(x+1)^2 and 2(x+ 1)(x¡2)

e 2(x+3)^2 and 4(x+ 3)(x¡7) f 4 x(x¡3) and 6 x(x¡3)^2

Write each term

as a product of

itsfactors!

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Y:\HAESE\IGCSE01\IG01_01\041IGCSE01_01.CDR Wednesday, 10 September 2008 2:07:22 PM PETER