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
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).