Polynomials are mathematical expressions consisting of variables (also called indeterminates) and coefficients, combined using only addition, subtraction, multiplication, and exponentiation to non-negative integer powers. They do not include division by variables. Each polynomial is made up of a finite number of terms, where each term is the product of a coefficient and variables raised to whole number exponents. For example, a polynomial in one variable xxx can be written as:

anxn+an−1xn−1+⋯+a2x2+a1x+a0,a_nx^n+a_{n-1}x^{n-1}+\dots +a_2x^2+a_1x+a_0,an​xn+an−1​xn−1+⋯+a2​x2+a1​x+a0​,

where the aia_iai​ are constants called coefficients, and nnn is a non- negative integer representing the degree of the polynomial

. Polynomials can have one or more variables and terms, such as:

• Single variable polynomial: x2−4x+7x^2-4x+7x2−4x+7
• Multivariable polynomial: x3+2xyz2−yz+1x^3+2xyz^2-yz+1x3+2xyz2−yz+1

They are classified based on the number of terms:

• Monomial: one term (e.g., x2x^2x2)
• Binomial: two terms (e.g., x2+1x^2+1x2+1)
• Trinomial: three terms (e.g., x3+23x+3x^3+\frac{2}{3}x+3x3+32​x+3)
• Polynomial: more than three terms

Polynomials are fundamental in many areas of mathematics and science, used to form polynomial equations, define polynomial functions, and approximate other functions in calculus and numerical analysis

. In summary, a polynomial is a finite sum of terms consisting of variables raised to non-negative integers, multiplied by coefficients, combined using addition, subtraction, and multiplication, but never division by a variable.