# Chapter 6 - Section 6.2 - Factoring Trinomials Whose Leading Coefficient is 1 - Exercise Set - Page 436: 73

$-2x(x-1)(x+4)$

#### Work Step by Step

Factoring the negative $GCF= -2x ,$ the given expression, $-2x^3-6x^2+8x ,$ is equivalent to \begin{array}{l}\require{cancel} -2x(x^2+3x-4) .\end{array} The trinomial expression above has $c= -4$ and $b= 3 .$ The possible factors of $c$ are $\{ 1,-4 \} ,\{ 2,-2 \} ,\{ -1,4 \} ,\{ -2,2 \}$. Among these factors, the pair whose sum is equal to $b$ is $\{ -1,4 \}.$ Hence, the factored form of the given expression is \begin{array}{l}\require{cancel} -2x(x-1)(x+4) .\end{array}

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