Chapter 8 - Section 8.3 - Solving Equations by Using Quadratic Methods - Exercise Set - Page 504: 87

$x^3-39x+70=0$

A polynomial equation that has solutions $\{2,5,-7\}$ is \begin{array}{l}\require{cancel} (x-2)(x-5)(x+7)=0 \\\\ [x(x)+x(-5)-2(x)-2(-5)](x+7)=0 \\\\ (x^2-5x-2x+10)(x+7)=0 \\\\ (x^2-7x+10)(x+7)=0 \\\\ x^2(x)+x^2(7)-7x(x)-7x(7)+10(x)+10(7)=0 \\\\ x^3+7x^2-7x^2-49x+10x+70=0 \\\\ x^3+(7x^2-7x^2)+(-49x+10x)+70=0 \\\\ x^3-39x+70=0 .\end{array}