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Factorize :
(i) x 3 - 3 x 2 + x - 3
(ii) a b 2 - (a - 1) b - 1
Solution :
(i) x 3 - 3 x 2 + x - 3 = x 2 (x - 3) + 1 (x - 3)
= (x - 3) (x 2 + 1)
(ii) a b 2 - (a - 1) b - 1 = a b 2 - a b + b - 1
= a b (b - 1) + 1 (b - 1)
= (b - 1) (a b + 1)