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

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Answer 1 · 2015-08-09T18:35:18

$(11x+1)(x-5)$

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

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

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

So we have:
$11x^2-54x-5=(11x+1)(x-5)$

How do you factor 11x^2-54x-511x^2-54x-5?