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

Here, $f(x)=3 x^{4}+17 x^{3}+9 x^{2}-7 x-10$

g(x) = x + 5

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

we should show ⟹ f(-5) = 0

here, x + 5 = 0

⟹ x = - 5

Substitute the value of x in f(x)

$f(-5)=3(-5)^{4}+17(-5)^{3}+9(-5)^{2}-7(-5)-10$

= (3 * 625) + (12 * (-125)) + (9*25) + 35 - 10

= 1875 - 2125 + 225 + 35 - 10

= 2135 - 2135

= 0

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