Factors-13
From Homeworkwiki
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)
