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.
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