Answer
$\pm 1,\pm2,\pm 3,\pm 6,\pm\frac{1}{2},\pm\frac{3}{2}$
Work Step by Step
We are given the polynomial function:
$$f(x)=2x^3+3x^2-11x-6.$$
First determine the factors of the constant term:
$$\pm 1, \pm 2, \pm 3, \pm 6.$$
Then determine the factors of the leading coefficient:
$$\pm 1,\pm 2.$$
The possible rational zeros are:
$$\pm\dfrac{1}{1},\pm\dfrac{2}{1}, \pm\dfrac{3}{1},\pm\dfrac{6}{1}.\pm\dfrac{1}{2},\pm\dfrac{2}{2},\pm\dfrac{3}{2},\pm\dfrac{6}{2}$$
Simplify to obtain the simplified list of possible rational zeros:
$$\pm 1,\pm2,\pm 3,\pm 6,\pm\dfrac{1}{2},\pm\dfrac{3}{2}.$$
