Intermediate Algebra (12th Edition)

$(a-4)(2a+1)$
$\bf{\text{Solution Outline:}}$ To factor the given expression, $2a^2-7a-4 ,$ use the factoring of trinomials in the form $ax^2+bx+c.$ $\bf{\text{Solution Details:}}$ In the trinomial expression above, $a= 2 ,b= -7 ,\text{ and } c= -4 .$ Using the factoring of trinomials in the form $ax^2+bx+c,$ the two numbers whose product is $ac= 2(-4)=-8$ and whose sum is $b$ are $\left\{ -8,1 \right\}.$ Using these two numbers to decompose the middle term results to \begin{array}{l}\require{cancel} 2a^2-8a+1a-4 .\end{array} Using factoring by grouping, the expression above is equivalent to \begin{array}{l}\require{cancel} (2a^2-8a)+(1a-4) \\\\= 2a(a-4)+(a-4) \\\\= (a-4)(2a+1) .\end{array}