How do you factor 6x² - x - 2?

1 Answer
George C.
May 26, 2015

Let's use the AC Method.

First multiply the coefficient (#A=6#) of the #x^2# term by the coefficient (#C=2#) of the constant term - ignoring the sign.

#AC = 6*2 = 12#

Notice that the sign of the constant (#C#) term is negative.

According to the AC Method, we need to look for a factorisation of our #AC# value into a pair of factors, whose difference is the middle coefficient #B=1#. Well #4 xx 3 = 12# and #4 - 3 = 1#. So the pair we want is #4# and #3#.

Now use this pair to split the middle term then factor by grouping:

#6x^2-x-2 = 6x^2-4x+3x-2#

#= (6x^2-4x)+(3x-2)#

#=2x(3x-2)+(3x-2)#

#=(2x-1)(3x-2)#

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