# How do you factor #6x^2+x-1# ?

##### 1 Answer

#### Explanation:

Here are a couple of methods (in no particular order):

**Method 1**

Note that:

#(ax+1)(bx-1) = abx^2+(b-a)x-1#

Comparing with:

#6x^2+x-1#

we want to find

The values

#6x^2+x-1 = (2x+1)(3x-1)#

**Method 2 - Completing the square**

To avoid much arithmetic with fractions, multiply first by

#24(6x^2+x-1) = 144x^2+24x-24#

#color(white)(24(6x^2+x-1)) = (12x)^2+2(12x)+1-25#

#color(white)(24(6x^2+x-1)) = (12x+1)^2-5^2#

#color(white)(24(6x^2+x-1)) = ((12x+1)-5)((12x+1)+5)#

#color(white)(24(6x^2+x-1)) = (12x-4)(12x+6)#

#color(white)(24(6x^2+x-1)) = (4(3x-1))(6(2x+1))#

#color(white)(24(6x^2+x-1)) = 24(3x-1)(2x+1)#

Divide both ends by

#6x^2+x-1 = (3x-1)(2x+1)#