# Polynomial Polynomial is an algebraic expression of the form aₙxⁿ + ... + a₃x³ + a₂x² + a₁x¹ + a₀x⁰ It is built from **terms** which are individual expressions connected with addition, starting with the lowest term on the right. Each term consists of a **constant** and a **variable** raised to a power. These constant are also called **coefficients**. The lowest term has the constant `a₀` and a variable `x` raised to 0. Each succeeding term (in right to left direction) must have a variable raised to ever increasing power, i.e. if the term's power is `k`, the power of the succeeding term must be `k+1`. axᵏ + bxᵏ⁻¹ + ... + ix³ + jx² + nx + m The lowest term collapses to the value of its constant, `a₀`, since its power is 0; the next term is `a₁x`, and form there on, a term may be elided only if its constant mutiplier is 0, which annihiltes the entire term. Examples: * `5x² + 3x + 6` = 5x² + 3x¹ + 6x⁰ * `42` = 42x⁰ = 42 \* 1 * `4x⁴ - 4` = 4x⁴ + 0x³ + 0x² + 0x¹ + 4 The only allowed operation for connecting the terms is addition, but since the terms might be nagative, the addition subsumes subtraction. **Degree** of a polynomial is determined by the term with the largest power. The one above is nth degree polynomial. --- # Agent Instructions: Querying This Documentation If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question. Perform an HTTP GET request on the current page URL with the `ask` query parameter: ``` GET https://mandober.gitbook.io/math-debrief/501-number-theory/terms/polynomial.md?ask= ``` The question should be specific, self-contained, and written in natural language. The response will contain a direct answer to the question and relevant excerpts and sources from the documentation. Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.