Question

SHOW that (x + 3) and (x - 2) are factors of f(x) = x4 + 10x3 + 23x2 - 34x - 120.

Answer 1

If f(x) = 0 then it is a root

x + 3 = 0
x=-3
f(-3) = (-3)^4 + 10(-3)^3 + 23(-3)^2 - 34(-3) - 120 = 0

x - 2 = 0
x=2
f(2) = (2)^4 + 10(2)^3 + 23(2)^2 - 34(2) - 120 = 0