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

Answer: 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