Intermediate Algebra (6th Edition)

$3x(5x-1)(2x+1)$
Factoring the $GCF= 3x ,$ the given expression, $30x^3+9x^2-3x ,$ is equivalent to \begin{array}{l}\require{cancel} 3x(10x^2+3x-1) .\end{array} Using the FOIL Method which is given by $(a+b)(c+d)=ac+ad+bc+bd,$ the expression above is equivalent to \begin{array}{l}\require{cancel} 3x(5x-1)(2x+1) .\end{array} Let \begin{array}{l}\require{cancel}Y_1= 30x^3+9x^2-3x \text{ and }\\Y_2= 3x(5x-1)(2x+1) .\end{array} Using a graphing calculator, the graph of $Y_1$ (dotted red graph) and $Y_2$ (solid blue graph) are given below. Since the two graphs coincide, then $Y_2$ and $Y_1$ are the same. That is, $Y_2$ is the correct factored form of $Y_1.$