# How do you factor 2x^2 -7x -4?

Oct 31, 2015

$2 {x}^{2} - 7 x - 4 = \left(2 x + 1\right) \left(x - 4\right)$

#### Explanation:

Start by hoping to find integer coefficient factors:

{: ("factors of " x^2 ,color(white)("XX"),"factors of constant",color(white)("XX"),"sum of"), ( "coefficient",color(white)("XX")," coefficient",color(white)("XX"),"cross product"), ((1,2),color(white)("XX"),(-1,4), color(white)("XX"), 1xx4+2xx(-1) = 6), ( ,color(white)("XX"),(1,-4), color(white)("XX"), 1xx(-4)+2xx(-1)=-2), ( ,color(white)("XX"),(-2,2), color(white)("XX"), 1xx2+2xx(-2) = -2), ( ,color(white)("XX"),(2,-2), color(white)("XX"), 1xx(-2)+2xx2=2), ( ,color(white)("XX"),(-4,1), color(white)("XX"), 1xx1+2x(-4)=-7), (,color(white)("XX"),(4,-1),color(white)("XX"), 1xx(-1)+2xx(4)= 7) :}

The pairs $\left(1 , 2\right) \mathmr{and} \left(- 4 , 1\right)$ give us the middle coefficient that we need.

Therefore the factors are:
$\textcolor{w h i t e}{\text{XXX}} \left(1 x - 4\right) \left(2 x + 1\right)$