What is a quartic polynomial function in standard form with zeros 1, -3,-2, and -2

x⁴ + 6x³ + 9x² - 4x - 12

Step-by-step explanation:

zeros are: x = 1, x = -3, x = -2, and x = -2

Which means: x - 1 = 0, x + 3 = 0, x + 2 = 0, and x + 2 = 0

So the factors are: (x - 1)(x + 3)(x + 2)(x + 2) = 0

Multiply two at a time:

    (x - 1)(x + 3) = x² + 2x - 3

    (x + 2)(x + 2) = x² + 4x + 4

Now multiply those polynomials together using distributive method:

 x²(x² + 4x + 4)  +2x(x² + 4x + 4)  -3(x² + 4x + 4)

= x⁴ + 4x³ + 4x² + 2x³ + 8x² + 8x - 3x² - 12x - 12

= x⁴ + 6x³ + 9x² - 4x - 12

Bonus: Quartic means a polynomial of degree 4