Chapter 3 - Polynomial and Rational Functions - 3.3 Zeros of Polynomial Functions - 3.3 Exercises - Page 337: 47

$x=2$ with a multiplicity of $3$, $x=\pm\sqrt 7$ each with a multiplicity of $1$

Step 1. Give $f(x)=(x-2)^3(x^2-7)$, we can find the first zero as $x=2$ with a multiplicity of $3$ Step 2. Let $(x^2-7)=0$, we have $x=\pm\sqrt 7$ each with a multiplicity of $1$