Polynomial equation

Definition

A polynomial equation is an algebraic expression set equal to zero, consisting of variables with non-negative integer exponents and coefficients. It takes the form $a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0 = 0$.

5 Must Know Facts For Your Next Test

1. The degree of a polynomial equation is determined by the highest power of the variable in the equation.
2. Polynomial equations can have multiple roots, which are solutions where the equation equals zero.
3. The Fundamental Theorem of Algebra states that every non-zero polynomial equation has at least one complex root.
4. Factoring is a common method used to solve polynomial equations, particularly those of lower degrees.
5. The Rational Root Theorem helps identify possible rational solutions for polynomial equations with integer coefficients.

Review Questions

• What determines the degree of a polynomial equation?
• How can you find the roots of a quadratic polynomial equation?
• What theorem guarantees that every non-zero polynomial equation has at least one complex root?

Related terms

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

Root: A solution to the polynomial equation where it equals zero.

Factoring: A method used to break down polynomials into simpler terms that can be multiplied together to obtain the original polynomial.