In each of the following, g(x) is a factor of polynomial f(x) or, not: f(x) = x^3 - 6x^2 - 19x + 84, g(x) = x - 7

Question

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

Answer 1

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).