# How do you factor by grouping t^3+2t^2-7t-14?

${t}^{3} + 2 {t}^{2} - 7 t - 14 = \left({t}^{3} + 2 {t}^{2}\right) - \left(7 t + 14\right)$
$= {t}^{2} \left(t + 2\right) - 7 \left(t + 2\right) = \left({t}^{2} - 7\right) \left(t + 2\right)$
So grouping the first two terms together and the last two terms together allows us to notice the common factor $\left(t + 2\right)$.
If we allow irrational coefficients, $\left({t}^{2} - 7\right)$ factors as $\left(t - \sqrt{7}\right) \left(t + \sqrt{7}\right)$.