Polynomial equation

Definition

A polynomial equation is an equation involving a polynomial expression, which sets the polynomial equal to zero. It can have one or more variables with non-negative integer exponents.

5 Must Know Facts For Your Next Test

1. The degree of a polynomial equation is determined by the highest power of the variable.
2. Polynomial equations can be classified into linear, quadratic, cubic, quartic, etc., based on their degree.
3. The Fundamental Theorem of Algebra states that every non-zero single-variable polynomial equation has at least one complex root.
4. Polynomial equations can be solved using various methods such as factoring, synthetic division, and the quadratic formula.
5. The roots or solutions of a polynomial equation are values for which the polynomial equals zero.

Review Questions

• What determines the degree of a polynomial equation?
• Name two methods used to solve polynomial equations.
• According to the Fundamental Theorem of Algebra, what can be said about the roots of a non-zero single-variable polynomial?

Related terms

Degree (of a Polynomial): The highest power of the variable in a polynomial expression.

Root (or Solution): A value that satisfies the polynomial equation when substituted for the variable.

Factoring:

A method used to solve polynomial equations by expressing the polynomial as a product of its factors.