SSC CGL Tier II 21 Sep 2014 Paper

Question : 50 of 100

Marks: +1, -0

If the L.C.M. and H.C.F. of two expressions are

(x ^2 + 6x + 8) (x + 1)

and

(x + 1)

respectively and one of the expressions is

x ^2 + 3x + 2

, find the other.

Solution:

(1)

x^{2}+6 x+8=x^{2}+4 x+2 x+8

=x(x+4)+2(x+4)

=(x+2)(x+4)

x^{2}+3 x+2=x^{2}+2 x+x+2

=x(x+2)+1(x+2)

=(x+2)(x+1)

First expression × Second expression = HCF × LCM
⇒

(x^2 + 3x + 2)

× Second expression
=

(x^2 + 6x + 8) (x + 1) × (x + 1)

⇒ (x + 2) (x + 1) × Second expression

= (x + 2) (x + 4) (x + 1) (x + 1)

⇒ Second expression

= {(x+2)(x+4)(x+1)(x+1)}/{(x+2)(x+1)}

=(x+4)(x+1)

=x^{2}+4 x+x+4=x^{2}+5 x+4

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