Answer: x⁴ + 6x³ + 9x² - 4x - 12
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