Question

The HCF of the polynomials \(x^3 - 3x^2 + x - 3\) and \(x^3 - x^2 - 9x +9\) is :

(a) x – 3 

(b) x – 1 

(c) x² + 1 

(d) (x - 1)(x - 3)

Answer 1

(a) x – 3

x³ - 3x² + x -3 = x² (x - 3) + 1(x - 3)

= (x - 3)(x² + 1)

x³ - x² -9x + 9 = x² (x - 1) - 9 (x - 1)

= (x² - 9)(x - 1) = (x + 3)(x + 3)(x - 1)

∴ Reqd. HCF = (x – 3)