Polynomial Solver

A polynomial is an algebraic expression consisting of variables and coefficients, using only addition, subtraction, and multiplication, with non-negative integer exponents. General Form: aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₁x + a₀ Where: • aᵢ = coefficients (constants) • n = degree (highest exponent) • x = variable • a₀ = constant term Classification by Degree: • Degree 0: Constant (e.g., 5) • Degree 1: Linear (e.g., 2x + 3) • Degree 2: Quadratic (e.g., x² + 5x + 6) • Degree 3: Cubic (e.g., x³ - 2x + 1) • Degree 4: Quartic • Degree 5: Quintic Fundamental Theorem of Algebra: A polynomial of degree n has exactly n roots (counting multiplicities) in the complex number system Key Operations: • Addition/Subtraction: Combine like terms • Multiplication: Distribute and combine • Division: Long division or synthetic division • Factoring: Express as product Solving Methods: • Factoring (when possible) • Rational Root Theorem • Synthetic Division • Quadratic Formula (degree 2) • Numerical Methods (higher degrees) Applications: Curve fitting, approximation, modeling natural phenomena, and computer graphics.