(x – 1) is a fact

We know that (x – 1) is a factor of the polynomial f(x) but it is not the factor of g(x).

Which means that, f(1) = 0 but g(1) ≠ 0.

But for (x - 1) to be a factor of the given options, when we put x=1 in the given functions we should get an answer as “0”.

So, for option (a), let F(x) = f(x) g(x)

To check whether (x – 1) is a factor of the polynomial F(x) we have to put x=1 in F(x) and see whether it gives us the answer as “0” or not.

F(1) = f(1) × g(1)

F(1) = 0 × g(1)

F(1) = 0

So, we can say that F(x) = f(x) g(x) is the polynomial whose factor is (x – 1).

⸫ (x – 1) will be the factor of f(x) g(x).

Hence the correct option is (a).