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)