# How do you factor #6x^3-6x^2-x+1#?

##### 2 Answers

Mar 23, 2018

Mar 23, 2018

#### Answer:

#### Explanation:

This cubic quadrinomial factors by grouping and using the difference of squares identity:

#A^2-B^2 = (A-B)(A+B)#

with

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

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

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

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

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