Use factor theorem to find whether polynomial g(x) is a factor of polynomial f(x), or not:

Here, $f(x)=x^{3}-6 x^{2}-19 x+84$

g(x) = x - 7

To prove that g(x) is the factor of f(x),

we should show ⟹ f(7) = 0

here, x - 7 = 0

⟹ x = 7

Substitute the value of x in f(x)

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

= 343 - (6 * 49) - (19 * 7) + 84

= 342 - 294 - 133 + 84

= 427 - 427

= 0

Since, the result is 0 g(x) is the factor of f(x)