How do you factor the expression #x^2 - x -6#?

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Answer 1 · 2018-03-04T06:38:55

The factored expression #(x+2)(x-3)#.

First, find two numbers that multiply to #-6# (the #c# value of the quadratic) and add up #-1# (the #b# value of the quadratic).

The two numbers are #-3# and #2#. Now, split #-x# into #-3x# and #2x#. Then, group together the two factors:

#color(white)=x^2-x-6#

#=x^2-3x+2x-6#

#=color(red)x*x-color(red)x*3+2x-6#

#=color(red)x*x-color(red)x*3+color(blue)2*x-color(blue)2*3#

#=color(red)x(x-3)+color(blue)2*x-color(blue)2*3#

#=color(red)x(x-3)+color(blue)2(x-3)#

#=(color(red)x+color(blue)2)(x-3)#

That's the factored quadratic.