problem_2_factoring.tex

\begin{problem}{factoring polynomials}

\question{Factor the polynomial $x^2 - 6x + 4x - 8$.}
\solution
{
\begin{align*}
    x^2 - 6x + 4x - 8 &= x^2 - 2x - 8        && \text{combine like terms} \\
                      &= x^2 - 4x + 2x - 8   && \text{split degree 1 term} \\
                      &= x(x - 4) + 2(x - 4) && \text{factor out $x$ and 2} \\
                      &= (x + 2)(x - 4)      && \text{factor out $x - 4$}
\end{align*}
}

\end{problem}