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

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

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Answer 1 · 2015-08-09T18:35:18

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

Explanation:

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

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

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

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

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

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