Question

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

Answer 1

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