# 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).

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