How do you factor the trinomial $x² - 5x - 6$ ?

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Answer 1 · 2015-11-25T12:04:19

$x^2-5x-6=(x-6)(x+1)$

We are hoping to find values $a$ and $b$ such that
$x^2-5x-6 = (x+a)(x+b) = (x^2+(a+b)x+ab)$

That is $ab= -6$
and $a+b=-5$

So we are looking for factors of $6$ (one negative and one positive to get $(-6)$ ) such that the difference between them is $5$

(and since we are trying for $(-5)$ as a sum, the larger of the two factors will be the negative one).

The only choices are:

${: ("factors of 6",,"sum of factors"), (1xx(-6),,-5), (2xx(-3),,-1) :}$

Fortunately the first pair gives us the values we need.

How do you factor the trinomial x² - 5x - 6x² - 5x - 6?