# How do you factor 11x^2-54x-5?

Aug 9, 2015

$\left(11 x + 1\right) \left(x - 5\right)$

#### Explanation:

Noting that 11 is a prime number we need a factorisation of the form:
$\left(11 x - a\right) \left(x - b\right) = 11 {x}^{2} - \left(11 b + a\right) x + a b$

So we need two numbers $a , b$ where:
$11 b + a = 54$
$a b = - 5$

By inspection we have:
$b = 5 , a = - 1$

So we have:
$11 {x}^{2} - 54 x - 5 = \left(11 x + 1\right) \left(x - 5\right)$