Question

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

Answer 1

If x+1 is a factor of f(x), then x=-1 is a zero of f(x).  This means f(-1) = 0.

With k in the function,

   f(-1) = 3(-1)^3 + 2(-1) + k

          = -3 -2 + k

          = -5 + k

If that has to equal 0, then k = 5.