Find all real and imaginary zeros of f(x) = x^3 + x^2 + 13x - 15, given that 1 is a zero of the function.

Would I use synthetic division? If so, how?

Any help is appreciated.

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The imaginary zeros are obtained from x^2+2x+15,

since this factor of the cubic does not itself have real factors,

it has complex factors since b^2<4ac.

x^2+2x+15 is zero for x = {-2+sqrt(4-60)}/2

and for x = {-2-sqrt(4-60)}/2,

which are x = -1+i(sqrt[14]) and x = -1-i(sqrt[14]).