# How do you factor 5n^2+10n+20?

May 19, 2015

y = 5(n^2 + 2n + 4)

The expression in parentheses can't be factored because D < 0

May 19, 2015

We must find its roots and then transform them into factors.

$\frac{- 10 \pm \sqrt{- 300}}{10}$
However, $\Delta = - 300$ indicates imaginary roots, because we can rewrite it as $300 \left(- 1\right)$, which will pave the way to find a solution.
We know, by imaginary numbers definition, that $\left(- 1\right) = {i}^{2}$. Therefore, $\sqrt{- 1} = i$ and we can proceed.
$\frac{- 10 \pm 10 i \sqrt{3}}{10}$=$- 1 \pm i \sqrt{3}$