Q. 75.0( 4 Votes )

# In each of the fo

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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