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.