Question

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

Answer 1

all possible rational roost are number of the form \(\frac{p}{q}\) where \(p\) divides the constant ( in your case 15) and \(q\) divides the leading coefficient, in your case 1

Answer 2

so the possibilites are
\[\pm1,\pm3,\pm5,\pm15\]

Answer 3

since you know 1 is a zero, you can factor it as
\[(x-1)(\text{something})\] and you can find the something by dividing, by synthetic division or by thinking

Answer 4

and to find all real and imaginary zeros

Answer 5

in this case you get
\[(x-1) (x^2+2 x+15)\] and the second part you can find the zeros using the quadratic formula
they are complex