# How do you factor 5n^2-4n-1?

##### 2 Answers
Apr 6, 2018

$\left(5 n + 1\right) \left(n - 1\right)$

Apr 6, 2018

(5n + 1)(n - 1)

#### Explanation:

Use the new AC Method (Socratic, Google Search)
$y = 5 {n}^{2} - 4 n - 1$
Converted trinomial:
$y ' = {n}^{2} - 4 n - 5$.
Method. Find the 2 factor numbers of y', then, divide them by a.
Find 2 numbers, that have opposite signs (ac < 0), knowing their sum (b = -4) and their product (ac = - 5). They are 1 and - 5.
Back to y, the factor-numbers are:
$n 1 = \frac{1}{a} = \frac{1}{5}$ and $n 2 = - \frac{5}{5} = - 1$
Factored form:
$y = 5 \left(n + \frac{1}{5}\right) \left(n - 1\right) = \left(5 n + 1\right) \left(n - 1\right)$