Chapter 4 - Polynomial and Rational Functions - 4.5 The Real Zeros of a Polynomial Function - 4.5 Assess Your Understanding - Page 234: 105

$-8, -4, -\frac{7}{3}$

Step 1 Find zeros of $f(x)=3x^3+16x^2+3x-10$ as $x=-5,-1,\frac{2}{3}$ (see figure). Step 2. As $f(x+3)$ can be obtained from $f(x)$ by shifting the curve 3 units to the left, we can find zeros for $f(x+3)$ as $x=-8, -4, -\frac{7}{3}$