Question

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

Answer 1

It is given that f(x) = x³ −6x² − 19x + 84, and  g(x) = x − 7

By the factor theorem, g(x) is the factor of polynomial f(x), if f (7) = 0.

Therefore, in order to prove that (x − 7) is a factor of f(x).

It is sufficient to show that f(7) = 0

Now,

`f(7) = (7)^3 - 6(7)^2 - 19(7) + 84`

        ` = 343 - 294 - 133 + 84`

        ` = 427 - 427`

        `=0`

Hence, (x − 7) is a factor of polynomial f(x).