Q. 44.0( 3 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}-19*x*+84, *g*(*x*) = *x*-7

Answer :

We have,

*f*(*x*) = *x*^{3}-6*x*^{2}-19*x*+84 and *g*(*x*) = *x*-7

In order to find whether g (x) = x – 7 is a factor of f (x) or not, it is sufficient to show that f (7) = 0

Now,

*f*(*x*) = *x*^{3}-6*x*^{2}-19*x*+84

f (7) = (7)^{3} – 6 (7)^{2} – 19 (7) + 84

= 343 – 294 – 133 + 84

= 0

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

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