What are the rational root(s) of 3x3 − 6x2 − x + 2 = 0?

Answer 1

We can factor by grouping here, which means grouping the first 2 terms and the last 2 terms of the left/hand side together and finding a common factor within each grouping:

(3x³ - 6x²) + (- x +2) = 0

3x² (x - 2) -1 (x - 2) = 0

(3x² - 1) (x - 2) = 0

(3x² - 1) = 0 or (x -2) = 0

x = ± √3/3 or x = 2 , the third of which is the only rational root.