Answer
In short, we have the following steps :
$1.$ List possible zeros
$2.$ Divide
$3.$ Repeat
Work Step by Step
As also explained in the chapter earlier, we have to do the following steps :
$1.$ List all the possible rational zeros, using the Rational Zeroes Theorem (Also explained in the chapter).
$2.$ Use synthetic division to evaluate the polynomial at each of the candidates for the rational zeros that you found in Step $1.$ When the remainder is $0$, note the quotient you have obtained.
$3.$ Repeat Steps $1$ and $2$ for the quotient. Stop when you reach a quotient that is quadratic or factors easily, and use the quadratic formula or factor to find the remaining zeros.
