Chapter 3 - Polynomial and Rational Functions - Section 3.2 The Real Zeros of a Polynomial Function - 3.2 Assess Your Understanding - Page 224: 35

$\pm1,\pm 3$

Let us consider that $m$ is a factor of the constant term and $n$ is a factor of the leading coefficient. Then the potential zeros can be expressed by the possible combinations as: $\dfrac{m}{n}$. We see from the given polynomial function that it has a constant term of $-3$ and a leading coefficient of $1$. The possible factors $m$ of the constant term and $n$ of the leading coefficient are: $m=\pm 1, \pm 3$ and $n=\pm 1$, Therefore, the possible rational roots of $f(x)$ are: $\dfrac{m}{n}=\pm1,\pm 3$