Answer :

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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