Sarthaks Test
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Find whether polynomial g(x) is a factor of polynomial f(x) or, not:

f(x) = x3 -6x2 +11x -6, g(x) = x2 -3x+2

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We have

f(x) = x3 -6x2 +11x -6 and g(x) = x2 -3x+2

g(x) = x2 -3x+2 = (x-1) (x-2)

Clearly (x-1) and (x-2) are factors of g(x)

In order to find whether g(x) = (x-1) (x-2) is a factor of f(x) or not, it is sufficient to prove that (x-1) and (x-2) are factors of f(x) . 

i.e., we should prove that f(1) = 0 and f(2) = 0

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