How do you factor 6x^3-6x^2-x+16x36x2x+1?

2 Answers
Mar 23, 2018

6x^3 - 6x^2 - x + 16x36x2x+1
=x(6x^2 - 6x -1 + 1)=x(6x26x1+1)
=x(6x^2 - 6x)=x(6x26x)
=6x(x^2 - x)=6x(x2x)

Mar 23, 2018

6x^3-6x^2-x+1 = (6x^2-1)(x-1)6x36x2x+1=(6x21)(x1)

color(white)(6x^3-6x^2-x+1) = (sqrt(6)x-1)(sqrt(6)x+1)(x-1)6x36x2x+1=(6x1)(6x+1)(x1)

Explanation:

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

A^2-B^2 = (A-B)(A+B)A2B2=(AB)(A+B)

with A=sqrt(6)xA=6x and B=1B=1 as follows:

6x^3-6x^2-x+1 = (6x^3-6x^2)-(x-1)6x36x2x+1=(6x36x2)(x1)

color(white)(6x^3-6x^2-x+1) = 6x^2(x-1)-1(x-1)6x36x2x+1=6x2(x1)1(x1)

color(white)(6x^3-6x^2-x+1) = (6x^2-1)(x-1)6x36x2x+1=(6x21)(x1)

color(white)(6x^3-6x^2-x+1) = ((sqrt(6)x)^2-1^2)(x-1)6x36x2x+1=((6x)212)(x1)

color(white)(6x^3-6x^2-x+1) = (sqrt(6)x-1)(sqrt(6)x+1)(x-1)6x36x2x+1=(6x1)(6x+1)(x1)