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.