Chapter 3 - Polynomial and Rational Functions - 3.3 Zeros of Polynomial Functions - 3.3 Exercises - Page 337: 48

$x=-1$ with a multiplicity of $2$ $x=1$ with a multiplicity of $3$ $x=\pm\sqrt {10}$ each with a multiplicity of $1$

Step 1. Give $f(x)=(x+1)^2(x-1)^3(x^2-10)$, we can find the first zero as $x=-1$ with a multiplicity of $2$ Step 2. We can find the second zero as $x=1$ with a multiplicity of $3$ Step 3. Let $(x^2-10)=0$, we have $x=\pm\sqrt {10}$ each with a multiplicity of $1$