Chapter 3, Polynomial and Rational Functions - Chapter 3 Review - Concept Check - Page 355: 8

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Step 1 List Possible Zeros: list all possible rational zeros, using the rational zeros theorem. The Rational Zero Theorem states that, if the polynomial $f(x)=a_{n}x^{n}+a_{n−1}x^{n−1}+...+a_{1}x+a_{0}$ has integer coefficients, then every rational zero of $f(x)$ has the form $p/q$ where $p$ is a factor of the constant term $a_{0}$ and $q$ is a factor of the leading coefficient $a_{n}$. When the leading coefficient is $1$, the possible rational zeros are the factors of the constant term. Step 2 Divide: 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. Step 3 Repeat Step 1 and Step 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.