Answer:
x^3 - 3x^2 - 4x + 12
Step-by-step explanation:
Okay, so let's work backwards.
3, -2, 2 are the zeros, so we can use these numbers write the equation in factored form. (For right now, as a placeholder, I'll let y = 0)
(x - 3)(x + 2)(x - 2) = 0
If you want to check this, you can insert each of the zeros into the expression with a constant of the opposite sign.
So now, we can just expand the factored form. (I'll be doing this one equation at a time)
(x - 3)(x + 2) = x^2 + 2x - 3x - 6 = x^2 - x - 6
(x^2 - x - 6)(x - 2) = x^3 - 2x^2 - x^2 + 2x - 6x + 12 = x^3 - 3x^2 - 4x + 12
So,
The equation in standard form is x^3 - 3x^2 - 4x + 12
(Don't take my word for it though, now that I've told you how, feel free to do it on your own)
