In each of the fo

We have,

f(x) = 3x⁴+17x³+9x²-7x-10 and g(x) = x+5

In order to find whether the polynomials g (x) = x – (-5) is a factor of f (x) or not, it is sufficient to show that f (-5) = 0

Now,

f(x) = 3x⁴+17x³+9x²-7x-10

f (-5) = 3 (-5)⁴ + 17 (-5)³ + 9 (-5)² – 7 (-5) – 10

= 3 * 625 + 17 * (-125) + 9 * 25 + 35 – 10

= 1875 – 2125 + 225 + 35 – 10

= 0

Hence, g (x) is a factor of f (x).