How do you factor 6x² - x - 2?

1 Answer
May 26, 2015

Let's use the AC Method.

First multiply the coefficient (A=6A=6) of the x^2x2 term by the coefficient (C=2C=2) of the constant term - ignoring the sign.

AC = 6*2 = 12AC=62=12

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

According to the AC Method, we need to look for a factorisation of our ACAC value into a pair of factors, whose difference is the middle coefficient B=1B=1. Well 4 xx 3 = 124×3=12 and 4 - 3 = 143=1. So the pair we want is 44 and 33.

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

6x^2-x-2 = 6x^2-4x+3x-26x2x2=6x24x+3x2

= (6x^2-4x)+(3x-2)=(6x24x)+(3x2)

=2x(3x-2)+(3x-2)=2x(3x2)+(3x2)

=(2x-1)(3x-2)=(2x1)(3x2)