A polynomial is a sum of terms, each a constant times a variable raised to a non-negative integer power. Examples: 3x² + 2x − 5, or 4y³ − y + 7. The highest exponent is the degree. Polynomials can be added, subtracted, multiplied, and sometimes divided.

Polynomials are among the simplest functions. Linear polynomials have degree 1, quadratics degree 2, cubics degree 3. Their graphs are smooth, continuous curves. The fundamental theorem of algebra says every polynomial of degree n has exactly n complex roots, counting multiplicity.

Polynomials approximate other functions. Taylor series express functions as infinite polynomials. In engineering, polynomial models fit data and simplify computation. In computer science, polynomial-time algorithms are considered efficient. The concept is central to algebra and analysis.

• Sum of terms with non-negative integer powers
• Degree is the highest exponent
• Fundamental theorem gives n complex roots
• Used in approximation and modeling