Answer
$\pm 1,\pm3,\pm 5,\pm 15$
Work Step by Step
We are given the polynomial function:
$$f(x)=x^3+9x^2+23x+15.$$
First determine the factors of the constant term:
$$\pm 1, \pm 3, \pm 5, \pm 15.$$
Then determine the factors of the leading coefficient:
$$\pm 1.$$
The possible rational zeros are:
$$\pm\dfrac{1}{1},\pm\dfrac{3}{1}, \pm\dfrac{5}{1},\pm\dfrac{15}{1}.$$
Simplify to obtain the simplified list of possible rational zeros:
$$\pm 1,\pm3,\pm 5,\pm 15.$$
