Chapter 3 - Polynomial and Rational Functions - Section 3.2 The Real Zeros of a Polynomial Function - 3.2 Assess Your Understanding - Page 224: 61

$x=\frac{1}{3},\pm\sqrt 5$

Step 1. For $3x^3-x^2-15x+5=0$, list possible rational real zeros $\frac{p}{q}: \pm1,\pm5,\pm\frac{1}{3},\pm\frac{5}{3}$ Step 2. Use synthetic division as shown in the figure to find zero(s) $x=\frac{1}{3}$. Step 3. Use the quotient to find other zeros: $3x^2-15=0 \Longrightarrow x=\pm\sqrt 5$