Answer:
x = ±i, x = -3, and x = -1
Step-by-step explanation:
If x = -1 is a solution, then x + 1 is a factor. Using grouping:
x⁴ + 4x³ + 4x² + 4x + 3 = 0
x⁴ + 4x³ + 3x² + x² + 4x + 3 = 0
x² (x² + 4x + 3) + x² + 4x + 3 = 0
(x² + 1) (x² + 4x + 3) = 0
(x² + 1) (x + 3) (x + 1) = 0
All the solutions are x = ±i, x = -3, and x = -1.
