Example  2
Factor each of the following binomials.

 

Original
(Expanded form)
 Find the GCF
Determine the other factor
Factored form
\(2x^2 - 10x\)               

\(6x^2y - 18xy\)


 

Original
(Expanded form)
 Find the GCF
Determine the other factor
Factored form
\(2x^2 - 10x\)  \(\begin{align}2x^2 &= {\color{red} 2 \cdot x} \cdot x \\
 10x &= {\color{red} 2} \cdot 5 \cdot {\color{red}x} \\
 {\rm{GCF}} &= \color{red}2x \\
 \end{align}\)
 \(\begin{align}
 \frac{{2x^2 - 10x}}{{2x}} &= \frac{{2x^2 }}{{2x}} - \frac{{10x}}{{2x}} \\
  &= x - 5 \\
 \end{align}\)
\(2x(x - 5) \)
\(6x^2y - 18xy\) \(\begin{align}
 6x^2y &= {\color{red} 2 \cdot 3 \cdot x} \cdot x \cdot \color{red} y \\
 18xy &= {\color{red}2 \cdot 3} \cdot 3 \cdot \color{red} x \cdot y \\
 {\rm{GCF}} &= {\color{red}2 \cdot 3 \cdot x \cdot y} = \color{red}6xy \\
 \end{align}\)
\(\begin{align}
 \frac{{6x^2y - 18xy}}{{6xy}} &= \frac{{6x^2y}}{{6xy}} - \frac{{18xy}}{{6xy}} \\
  &= x - 3 \\
 \end{align}\)
\(6xy(x - 3) \)