Example7.4.4

Factor \(10x^2+23x+6\text{.}\)

  1. \(10\cdot6=60\)

  2. Use a list of factor pairs for \(60\) to find that \(3\) and \(20\) are a pair that sums to \(23\text{.}\)

  3. Intentionally break up the \(23\) as \(3+20\text{:}\)

    \begin{align*} \amp10x^2\overbrace{{}+23x}+6\\ \amp=10x^2\overbrace{{}+3x+20x}+6\\ \amp=\left(10x^2+3x\right)+(20x+6)\\ \amp=x\highlight{(10x+3)}+2\highlight{(10x+3)}\\ \amp=\highlight{(10x+3)}(x+2) \end{align*}
in-context