Chapter 5 - Polynomials and Factoring - 5.6 Factoring: A General Strategy - 5.6 Exercise Set - Page 344: 14

$(x+3)(x+2)(x-2)$

Using factoring by grouping, the factored form of the given expression, $ x^3+3x^2-4x-12 ,$ is \begin{array}{l} (x^3+3x^2)-(4x+12) \\\\= x^2(x+3)-4(x+3) \\\\= (x+3)(x^2-4) .\end{array} Using $a^2-b^2=(a+b)(a-b)$, the expression above is further factored as \begin{array}{l} (x+3)(x+2)(x-2) .\end{array}