Q. 11 C5.0( 6 Votes )
(x – 1) is a factor of the polynomial f(x) but it is not the factor of g(x). So (x – 1) will be a factor of
A. f(x) g(x)
B. –f(x) + g(x)
C. f(x) –g(x)
D. {f(x) + g(x)}g(x)
Answer :
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).
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