Concept of Polynomial and Its Roots

A single variable polynomial is an algebraic expression that contains only one variable (usually x), and the powers of the variable are non-negative integers.

General form

where:

• x = the single variable
• a₀, a₁, …, a_n = constants / coefficients
• n = a non-negative integer

A polynomial is said to be in standard form when the terms are arranged in ascending or descending order of the powers of the variable.

For example: p(x) = 2x⁴ − 5x³ + 3x² + 5x − 4 is in standard form, because the powers of all terms are arranged in descending order. Similarly, q(x) = 2x⁴ + 3x² − 4 can be written in standard form by including the missing terms with zero coefficients, i.e. q(x) = 2x⁴ + 0·x³ + 3x² + 0·x − 4.

The degree of a polynomial is the highest power of the variable in the polynomial.

The coefficient of the highest degree term is called the leading coefficient.