Question

Factor the quadratic expression $p^2-5p-14$ completely.

Answer 1

Factor the quadratic polynomial ${\mathit{p}}^{\mathbf{2}}\mathbf{-}\mathbf{5}\mathit{p}\mathbf{-}\mathbf{14}$:

Find the product of the quadratic term $p^2$ and the constant term $-14$, $p^2\times \left(-14\right)=-14p^2$ . Through a hit and trial process, we have to find two factors of $-14p^2$ that add up to give the linear term $-5p$. The two factors that satisfy these conditions are $-7p$ and $2p$, because their sum is equal to the linear term $-5p$ and their product is equal to $-14p^2$.

Rewrite term $-5p$ in the expression $p^2-5p-14$ as $-7p+2p$.

Then factorize by grouping the terms:

$\begin{array}{rcl}{p}^2-5p-14& =& p^2-7p+2p-14\\ & =& p\left(p-7\right)+2\left(p-7\right)\\ & =& \left(p-7\right)\left(p+2\right)\end{array}$

Thus, $p^2-5p-14$ is completely factorized to obtain $\left(p-7\right)\left(p+2\right)$.