# 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) = x3-6x2-19x+84, g(x) = x-7

We have,

f(x) = x3-6x2-19x+84 and g(x) = x-7

In order to find whether g (x) = x – 7 is a factor of f (x) or not, it is sufficient to show that f (7) = 0

Now,

f(x) = x3-6x2-19x+84

f (7) = (7)3 – 6 (7)2 – 19 (7) + 84

= 343 – 294 – 133 + 84

= 0

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

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