# Chapter 5 - Section 5.4 - Factoring Trinomials - Exercise Set - Page 361: 71

$2x^{2}(4x-1)(3x+2)$

#### Work Step by Step

$24x^{4}+10x^{3}-4x^{2}\qquad$...factor out the common term, $2x^{2}$. $=2x^{2}(12x^{2}+5x-2)$ Two factors of $ac=-24$, whose sum is $b=+5$ are$-3$ and $8$. Rewrite $5x$ as $-3x+8x$ and factor in pairs. $24x^{4}+10x^{3}-4x^{2}$ $=2x^{2}(12x^{2}-3x+8x-2)$ $=2x^{2}[3x(4x-1)+2(4x-1)]$ =$2x^{2}(4x-1)(3x+2)$

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