Polynomial Definition and Example | Types of Polynomial

A polynomial is a mathematical expression built from variables, numbers and the operations of addition, subtraction and multiplication. It never divides by a variable and never uses a negative or fractional exponent on a variable.

Standard form

A polynomial in x is usually written as aₙxⁿ + aₙ₋₁xⁿ⁻¹ + … + a₁x + a₀, where the a values are constants and n is a whole number.

Examples and non-examples

Examples: 3x² + 2x + 5, 7x³ − 4x + 9, and even a single number such as 6. Non-examples: 1/x, x⁻² + 3, and √x + 2, because each breaks one of the rules above.

Types by number of terms

Monomial: one term, such as 5x. Binomial: two terms, such as x + 3. Trinomial: three terms, such as x² + 3x + 2.

Types by degree

The degree is the highest exponent. Degree 0 is constant, degree 1 is linear, degree 2 is quadratic, degree 3 is cubic, and higher degrees follow the same pattern.

Learn more

For a video explanation of this topic, see Khan Academy Algebra course.