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

Question

Philoid · Accepted Answer

We have,

f(x) = x³-6x²-19x+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) = x³-6x²-19x+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).

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) = x3-6x2-19x+84, g(x) = x-7

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) = x³-6x²-19x+84, g(x) = x-7