Answer
$x=1, -3\pm\sqrt {11}$
Work Step by Step
Step 1. List the possible rational zeros as
$\frac{p}{q}=\pm1,\pm2$
Step 2. Use synthetic division to find a zero at $x=1$ as shown in the figure.
Step 3. With the quotient $x^2+6x-2$, we can obtain the other two zeros as
$x=\frac{-6\pm\sqrt {36+8}}{2}=-3\pm\sqrt {11}$
Step 4. We conclude that the zeros are
$x=1, -3\pm\sqrt {11}$
