Answer :

We have,

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


In order to find g (x) = x2-3x+2 = (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 have to prove that f (1) = 0 and f (2) = 0


f (1) = (1)3 – 6 (1)2 + 11 (1) – 6


= 1 – 6 + 11 – 6


= 12 – 12


= 0


f (2) = (2)3 – 6 (2)2 + 11 (2) – 6


= 8 – 24 + 22 – 6


= 30 – 30


= 0


Since, (x – 1) and (x – 2) are factors of f (x).


Therefore, g (x) = (x – 1) (x – 2) are the factors of f (x).


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