What is a polynomial function in standard form with zeroes 1, 2, -2. and -3 a. x^4 + 2x^3 + 7x^2 - 8x + 12 b. x^4 + 2x^3 - 7x^2 - 8x + 12 c. x^4 + 2x^3 - 7x^2 + 8x + 12 d. x^4 + 2x^3 + 7x^2 + 8x + 12

A polynomial with the given zeros can be represented as
   f(x) = (x-1)(x-2)(x+2)(x+3).
   Note that if you set f(x) = 0, then 1,2,-2, and -3 certainly are the solutions. From here, we simply multiply/expand out the polynomial. We can do this in a variety of ways, one of which is taking the left two and right two products separately. We have
   (x-1)(x-2) = x^2 - 3x + 2
   and
   (x+2)(x+3) = x^2 + 5x + 6.
   This gives that
   f(x) = (x^2 - 3x + 2) (x^2 + 5x + 6).
   Expanding this expression out then gives us our answer as
    f(x) = x^4 + 2x^3 - 7x^2 - 8x + 12
   or answer choice B.