Question

list all the possible rational zeros of f using the rational zero theorem. Then find all the zeros of the function.

f(x)=x^3+4x^2+9x+36

Answer 1

So I tried -4 and it worked. So that is so far my zero of f.

so is this the right way to write the equation in order to find those zeros.

f(x)=(x+4)(x^2+0+9) ?? cuz if you do synthetic division, you would subtract 4 from 4 to get zero which is the middle term. or should it not be in the equation. and be f(x)=(x+4)(x^2+9)

Answer 2

Yes it is
(x+4)(x^2+9)

x = -4 you know
however
x^2+9 = 0
x^2 = -9
is x = +3i or x = -3i (not rational real)