Beginning Algebra With Applications, Chapter 8, 8.2, Section 8.2, Problem 118

State whether or not the trinomial has a factor of $(x+y)$.

a. $2x^2 - 2xy - 4y^2$


$
\begin{equation}
\begin{aligned}

2x^2 - 2xy - 4y^2 =& 2 \left(x^2 -xy-2y^2 \right)
&& \text{Factor out } 2
\\
=& 2 (x-2y)(x+y)
&& \text{Factor } x^2 - xy -2y^2

\end{aligned}
\end{equation}
$


The trinomial $2x^2 - 2xy - 4y^2$ has a factor of $(x+y)$.

b. $2x^2 y - 4xy - 4y$

$2x^2 y - 4xy - 4y = 2y(x^2 - 2x - 2) \qquad$ Factor out $2y$

The trinomial $2x^2y - 4xy - 4y$ is not a factor of $(x+y)$.