Posted by: Suyash D. on 14.03.2021
Ask a QuestionAns. Option a) f(x).g(x)
Reason: f(x).g(x) is the only polynomial given, which already contains the factor (x-2).
Answer: It is given that (x-2) is a factor of f(x) but not a factor of g(x). This means that (x-2) is not a common factor between f(x) and g(x). In that case (x-2) can only be a factor of f(x)*g(x) or f(x) /g(x). Out of the four options given only option (a) satisfies this condition. Hence the correct answer is option (a).
If x-2 is a facor of f(x) but not g(x), it means f(x) must contain (x-2) term in it as
f(x)=(x-2)f1(x) but g(x ) dos not contain any facor of (x-2)
so when f(x) is multiply anyone its alsohas a factor of x-2.
i.e. f(x)g(x) has factor of (x-2) and
so final answer is Option A
if (x -2) is a factor of polynomial f(x) but not of g(x),then it must be a factor of multiplication of f(x) and g(x). i.e f(x)g(x).
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