Factors-13

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Factorize :

(i) a 2 + 1 / a 2 - 2 + 5 a - 5 / a

(ii) x 2 + (a 2 - 1) x / a - 1

Solution :

(i) a 2 + 1 / a 2 - 2 + 5 a - 5 / a

= ( a 2 + 1 / a 2 - 2 ) + 5 (a - 1 / a)

= (a - 1 / a) 2 + 5 (a - 1 / a)

= (a - 1 / a) (a - 1 / a + 5)

(ii) x 2 + (a 2 - 1) x / a - 1

= x 2 + (a 2 / a - 1 / a) x - 1

= x 2 + a x - x / a - 1

= (x 2 - x / a) + (a x - 1)

= x (x - 1 / a) + a (x - 1 / a)

= (x - 1 / a) (x + a)

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