Step 1:

Remainder theorem:

When we divide a polynomial by the remainder equals .

The polynomial

If p /q is a rational zero, then p is a factor of 8 and q is a factor of 1.

The possible values of p are  ± 1, ± 2, ± 4 and  ± 8.

The possible values for q are ± 1.

So, p/q = ± 1, ± 2, ± 4 and  ± 8.

Make a table for the synthetic division and test possible  zeros.

is not a factor of 

is a factor of

Step 2:

Since , is a zero. The depressed polynomial is  .

Since the depressed polynomial of this zero, , is quadratic, use the Factorization to find the roots of the related quadratic equation .

and

and

Solution:

Factoring of .