Question

In each of the following, use factor theorem to find whether polynomial g(x) is a factor of polynomial f(x) or, not:
f(x) = x³-6x²+11x-6, g(x) = x-3

Answer 1

g(x) = x-3 is a factor of f(x) = x³-6x²+11x-6

The remaining factors of the polynomial f(x) = x³-6x²+11x-6, other than g(x) = x-3 are (x-1) (x-2)

Given,

f(x) = x³-6x²+11x-6

g(x) = x-3

⇒ x = 3

Given g(x) is a factor of polynomial f(x) = x³-6x²+11x-6, then, g(x) value should satisfy the polynomial f(x).

f(3) =  (3)^3 - 6(3)^2 + 11(3) - 6

= 27 - 54 + 33 - 6

= 0

Hence g(x) is a factor of the polynomial f(x).