Polynomial

Definition

A polynomial is an algebraic expression consisting of variables, coefficients, and non-negative integer exponents. It can be written in the form $a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0$ where $a_n, a_{n-1}, ..., a_1, a_0$ are constants and $n$ is a non-negative integer.

5 Must Know Facts For Your Next Test

1. The degree of the polynomial is the highest exponent in the expression.
2. The leading coefficient is the coefficient of the term with the highest degree.
3. Polynomials can have real or complex roots, also known as zeros.
4. The Fundamental Theorem of Algebra states that every non-zero polynomial has at least one complex root.
5. Polynomial division can be performed using long division or synthetic division.

Review Questions

• What is the degree and leading coefficient of the polynomial $3x^4 - 2x^3 + x - 5$?
• How many roots can a polynomial of degree five have?
• Explain how you would use synthetic division to divide $2x^3 - x^2 + 3x - 1$ by $x - 2$.

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.

Zeros:

Values of $x$ that make the polynomial equal to zero; also known as roots.