2x^3 - x2 - 6x + 3 = x^2(2x - x) - 3(2x - 1) = (2x - 1)(x^2 - 3) = (2x - 1)(x - √3)(x + √3)

the factored form of the polynomial is:

f(x) = (2x - 1)(x - √3)(x + √3)

the x-intercepts of the polynomial happens for the values for x such that f(x) = 0:

f(x) = 0 that is (2x - 1)(x - √3)(x + √3) = 0 if

2x - 1 = 0

x = 1/2

or

x - √3 = 0

x = √3

or

x + √3 = 0

x = - √3

the x-intercepts of the polynomial are: (1/2, 0), (√3, 0) and (-√3, 0).