In each of the following, g(x) is a factor of polynomial f(x) or, not: f(x) = x^3 - 6x^2 + 11x - 6, g(x) = x - 3

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

We have,

f(x) = x³ - 6x² + 11x - 6 and g(x) = x - 3

In order to find whether polynomials g (x) = x – 3 is a factor of f (x), it is sufficient to show that f (3) = 0

Now,

f(x) = x³ - 6x² + 11x - 6

f (3) = 3³ – 6 (3)² + 11 (3) – 6

= 27 – 54 + 33 – 6

= 60 – 60

= 0

Hence, 

g (x) is a factor of f (x).