Polynomial

Definition

A polynomial is an algebraic expression composed of variables and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents. Examples include $3x^2 + 2x - 1$ and $5y^3 - y + 4$.

5 Must Know Facts For Your Next Test

1. A polynomial's degree is the highest power of its variable.
2. The leading coefficient is the coefficient of the term with the highest degree.
3. The zeros or roots of a polynomial are values of the variable that make the polynomial equal to zero.
4. Polynomials can be added, subtracted, multiplied, and divided (excluding division by zero).
5. The Fundamental Theorem of Algebra states that a polynomial of degree $n$ has exactly $n$ complex roots.

Review Questions

• What is the degree of the polynomial $7x^4 - 2x^3 + x - 5$?
• How do you find the zeros of a polynomial function?
• What does the leading coefficient tell you about a polynomial?

Related terms

Degree: The highest power of the variable in a polynomial.

Leading Coefficient: The coefficient of the term with the highest degree in a polynomial.

Fundamental Theorem of Algebra: States that every non-constant single-variable polynomial with complex coefficients has at least one complex root.