Q8 of 32 Page 2

If a is a zero of polynomial f(x) and (x – b) is the factor of polynomial g(x). Find value of a.g(b) – b. f(a)

Concept Used:


Factor theorem: If (x – a) is a factor of f(x), then f(a) = 0


Explanation:


a is a zero of f(x), therefore, f(a) = 0


As (x – b) is a factor of g(x), g(b) = 0


Therefore,


a.g(b) – b.f(a) = a.0 – b.0 = 0


Hence, a.g(b) – b.f(a) = 0


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