How do you factor the trinomial 5x^2 − 2x − 7?

Dec 7, 2015

$5 {x}^{2} - 2 x - 7$ factors to $\left(5 x + 1\right) \left(x - 7\right)$

Explanation:

Since both 5 and 7 are prime,
the only options for
$5 {x}^{2}$ are $1 x$ and $5 x$,

and the only options for
$- 7$ are $- 1$ and $7$ or $1$ and $- 7$

Notice that the middle term is $- 2 x$ and to get that we would need to have had $5 x - 7 x$, before simplifying the middle term.

So to get this is a factored form it would be
$\left(5 x - 1\right) \left(x + 7\right)$