On the y-axis, x = 0. Thus, we have:
F(0) = 2(0)^3 + 3(0)^2 - 8(0) + 3 = 0 + 0 - 0 + 3 = 3
Thus, (0, 3) is the y-intercept.
On the x-axis, y = 0. Thus, we have:
0 = 2x^3 + 3x^2 - 8x + 3
0 = 2x^3 + 5x^2 - 2x^2 - 3x - 5x + 3
0 = 2x^3 + 5x^2 - 3x - 2x^2 - 5x + 3
0 = (2x^3 + 5x^2 - 3x) - (2x^2 + 5x - 3)
0 = x(2x^2 + 5x - 3) - 1(2x^2 + 5x - 3)
0 = (x - 1)(2x^2 + 5x - 3)
0 = (x - 1)(2x^2 - x + 6x - 3)
0 = (x - 1)((2x^2 - x) + (6x - 3))
0 = (x - 1)(x(2x - 1) + 3(2x - 1))
0 = (x - 1)(x + 3)(2x - 1)
x - 1 = 0 or x + 3 = 0 or 2x - 1 = 0
x = 1 or x = -3 or x = 1/2
Thus, the x-intercepts are (1, 0), (-3, 0) and (1/2, 0).