Question

coefficients for the polynomial with degree 3, roots: x = 2, x = -1, and x = 3, and with a leading coefficient of 1

Answer 1

I suppose you want
f(x) = (x-2)(x+1)(x-3)
expand if you feel there is a need to do that.

Answer 2

(x-2)(x+1)(x-3) = 0
(x-2)(x^2 -2x -3) = 0
x^3 - 2x^2 - 3x - 2x^2 + 4x + 6 = 0
so y = x^3 - 4x^2 + x + 6
check one root, what happens when x= 2 ?
y = 8 - 16 + 2 + 6 = 0 .... Whew :)