Answer
$x=1, -3\pm\sqrt {11}$
![](https://gradesaver.s3.amazonaws.com/uploads/solution/37478dab-9854-4ae6-ae59-354ef26d1e86/result_image/1582856344.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T021705Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=78da77b7ba90bbe09d086e2ca1ae8b9c0a54c303b0d9246ef5f2075d3602093b)
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
$x=1, -3\pm\sqrt {11}$