Cambridge International Mathematics

50 Algebra (Expansion and factorisation) (Chapter 1)

Example 32 Self Tutor

Factorise: a x^2 ¡ 2 x¡ 15 b x^2 +x¡ 6

a sum=¡ 2 and product=¡ 15

) the numbers are¡ 5 and+3

) x^2 ¡ 2 x¡15 = (x¡5)(x+3)

b sum=1 and product=¡ 6

) the numbers are+3and¡ 2

) x^2 +x¡6=(x+ 3)(x¡2)

Example 33 Self Tutor

Fully factorise by first removing a common factor: 3 x^2 +6x¡ 72

3 x^2 +6x¡ 72

=3(x^2 +2x¡24)

=3(x+ 6)(x¡4)

ffirst look for acommon factorg

fsum=2, product=¡ 24

) the numbers are 6 and¡ 4 g

Example 34 Self Tutor

Fully factorise by first removing a common factor: 77 + 4x¡x^2

77 + 4x¡x^2

=¡x^2 +4x+77

=¡1(x^2 ¡ 4 x¡77)

=¡(x¡11)(x+7)

frewrite in descending powers ofxg

fremove¡ 1 as a common factorg

fsum=¡ 4 , product=¡ 77

) the numbers are¡ 11 and 7 g

EXERCISE 1K

1 Find two numbers which have:

a product 12 and sum 7 b product 15 and sum 8 c product 16 and sum 10

d product 18 and sum 11 e product¡ 21 and sum 4 f product¡ 21 and sum¡ 4

g product¡ 12 and sum¡ 4 h product¡ 30 and sum 13 :

2 Factorise:

a x^2 +4x+3 b x^2 +14x+24 c x^2 +10x+21

d x^2 +15x+54 e x^2 +9x+20 f x^2 +8x+15

g x^2 +10x+24 h x^2 +9x+14 i x^2 +6x+8

3 Factorise:

a x^2 ¡ 3 x+2 b x^2 ¡ 4 x+3 c x^2 ¡ 5 x+6

d x^2 ¡ 14 x+33 e x^2 ¡ 16 x+39 f x^2 ¡ 19 x+48

g x^2 ¡ 11 x+28 h x^2 ¡ 14 x+24 i x^2 ¡ 20 x+36

The product is

negative and the

numbers are

opposite in sign.

Always look for

common factorsfirst.

IGCSE01

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Y:\HAESE\IGCSE01\IG01_01\050IGCSE01_01.CDR Tuesday, 7 October 2008 12:46:42 PM PETER