Given f (x) = x^3+4x^2+5x+2 and that - 1 is a zero of f (x). What is the factor of f (x)

From the context, the question is asking "What are the factors of f (x) ".

As Sxerks indicated in the comments, (x-1) is a root = > (x+1) is a factor.

To factor completely, a long division or synthetic division can be done to find

f (x) / (x+1) = (x^3+4x^2+5x+2) / (x+1) = x^2+3x+2 with no remainder.

Factor the resulting quadratic,

x^2+3x+2 = (x+2) (x+1)

factors f (x) completely into

f (x) = (x+1) ^2 (x+2)