How do you factor 6x^3-6x^2-x+16x3−6x2−x+1?
2 Answers
Explanation:
This cubic quadrinomial factors by grouping and using the difference of squares identity:
A^2-B^2 = (A-B)(A+B)A2−B2=(A−B)(A+B)
with
6x^3-6x^2-x+1 = (6x^3-6x^2)-(x-1)6x3−6x2−x+1=(6x3−6x2)−(x−1)
color(white)(6x^3-6x^2-x+1) = 6x^2(x-1)-1(x-1)6x3−6x2−x+1=6x2(x−1)−1(x−1)
color(white)(6x^3-6x^2-x+1) = (6x^2-1)(x-1)6x3−6x2−x+1=(6x2−1)(x−1)
color(white)(6x^3-6x^2-x+1) = ((sqrt(6)x)^2-1^2)(x-1)6x3−6x2−x+1=((√6x)2−12)(x−1)
color(white)(6x^3-6x^2-x+1) = (sqrt(6)x-1)(sqrt(6)x+1)(x-1)6x3−6x2−x+1=(√6x−1)(√6x+1)(x−1)