Chapter 3 - Polynomial and Rational Functions - Section 3.2 The Real Zeros of a Polynomial Function - 3.2 Assess Your Understanding - Page 224: 63

$x=-3,-2$.

Step 1. For $x^4+4x^3+2x^2-x+6=0$, list possible rational real zeros $\frac{p}{q}: \pm1,\pm2,\pm3,\pm6$ Step 2. Use synthetic division as shown in the figure to find zero(s) $x=-3,-2$. Step 3. Use the quotient to find other zeros: $x^2-x+1=0$, no real solutions.