Q. 14.4( 11 Votes )

# In each of the following, use factor theorem to find whether polynomial *g*(*x*) is a factor of polynomial *f*(*x*) or, not:

*f*(*x*) = *x*^{3}-6*x*^{2}+11*x*-6, *g*(*x*) = *x*-3

Answer :

We have,

*f*(*x*) = *x*^{3}-6*x*^{2}+11*x*-6 and *g*(*x*) = *x*-3

In order to find whether polynomials g (x) = x – 3 is a factor of f (x), it is sufficient to show that f (3) = 0

Now,

*f*(*x*) = *x*^{3}-6*x*^{2}+11*x*-6

f (3) = 3^{3} – 6 (3)^{2} + 11 (3) – 6

= 27 – 54 + 33 – 6

= 60 – 60

= 0

Hence, g (x) is a factor of f (x).

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