Question

Given f(x)=x^3+2x+k.
and x+1 is a factor of f(x), then what is the value of k?

Answer 1

k = 3.

Explanation:

By the Factor Theorem. if x+a is a factor of f(x) then f(-a) = 0.

Here we use f(-1):

f(-1) = (-1)^3 + 2(-1) + k = 0

-1 - 2 + k = 0

k = 3.