generate a polynomial from the roots -3,2,1,2,3

To generate a polynomial from the given roots, we first need to determine the factors of the polynomial. Since the roots are -3, 2, 1, 2, and 3, the factors of the polynomial are:

(x + 3)(x - 2)(x - 1)(x - 2)(x - 3)

To find the polynomial itself, we multiply these factors:

(x + 3)(x - 2)(x - 1)(x - 2)(x - 3)
= (x^2 + x - 6)(x - 1)(x - 2)(x - 3)
= (x^3 - 3x^2 - 3x + 9)(x - 2)(x - 3)
= (x^4 - 5x^3 + 3x^2 + 47x - 54)

Therefore, the polynomial with roots -3, 2, 1, 2, and 3 is:

f(x) = x^4 - 5x^3 + 3x^2 + 47x - 54