Understanding Polynomial Functions
Key Features of Polynomials:
A polynomial function p(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₁x + a₀ has:
End Behavior:
| Degree | Leading Coeff | As x → -∞ | As x → +∞ |
| Even | Positive | f(x) → +∞ | f(x) → +∞ |
| Even | Negative | f(x) → -∞ | f(x) → -∞ |
| Odd | Positive | f(x) → -∞ | f(x) → +∞ |
| Odd | Negative | f(x) → +∞ | f(x) → -∞ |
Multiplicity of Zeros:
Factored Form Advantage:
p(x) = a(x - r₁)^m₁ · (x - r₂)^m₂ · ... reveals: