Chapter 3 - Polynomial and Rational Functions - Section 3.2 The Real Zeros of a Polynomial Function - 3.2 Assess Your Understanding - Page 224: 62

$x=-\frac{1}{2},2,4$

Step 1. For $2x^3-11x^2+10x+8=0$, list possible rational real zeros $\frac{p}{q}: \pm1,\pm2,\pm4,\pm8,\pm\frac{1}{2}$ Step 2. Use synthetic division as shown in the figure to find zero(s) $x=2$. Step 3. Use the quotient to find other zeros: $2x^2-7x-4=0 \Longrightarrow (2x+1)(x-4)=0 \Longrightarrow x=-\frac{1}{2},4$