Answer 1

It is given that f(x) = x⁵ + 3x⁴ − x³ − 3x² + 5x + 15 and g(x) = x+3 

By the factor theorem, g(x) is the factor of polynomial f(x).

i.e. x+3 =0

 `f(-3) = (-3)^5 + 3(-3)^4 - (-3)^3 - 3(- 3)^2 + 5(-3) + 15`
f (−3) = 0

Hence, g(x) is the factor of polynomial f (x).