Factor Quadratic Trinomials with Leading Coefficient Other than 1: example 7.30

Use the preliminary strategy.

$\begin{array}{cccc}\text{Is there a greatest common factor?}\hfill & & & 2n^2-8n-42\hfill \\ \text{Yes, GCF = 2. Factor it out.}\hfill & & & 2\left(n^2-4n-21\right)\hfill \\ \text{Inside the parentheses, is it a binomial, trinomial, or are there}\hfill & & & \\ \text{more than three terms?}\hfill & & & \\ \text{It is a trinomial whose coefficient is 1, so undo FOIL.}\hfill & & & 2\left(n\right)\left(n\right)\hfill \\ \text{Use 3 and}\mathrm{-7}\text{as the last terms of the binomials.}\hfill & & & 2\left(n+3\right)\left(n-7\right)\hfill \end{array}$

Check.

$2\left(n+3\right)\left(n-7\right)$

$2(n^2-7n+3n-21)$

$2(n^2-4n-21)$

$2n^2-8n-42✓$