Binomial

Definition

A binomial is a polynomial with exactly two distinct terms, typically expressed in the form $a + b$ where $a$ and $b$ are constants or variables.

5 Must Know Facts For Your Next Test

1. A binomial can be written as the sum or difference of two monomials.
2. The degree of a binomial is determined by the term with the highest power.
3. Common operations involving binomials include addition, subtraction, multiplication, and division.
4. The Binomial Theorem provides a method to expand expressions of the form $(a+b)^n$.
5. Factoring binomials often involves recognizing patterns such as difference of squares: $(a^2 - b^2 = (a - b)(a + b))$.

Review Questions

• What defines a polynomial as a binomial?
• How would you find the degree of the binomial $3x^2 + 2x$?
• Use the Binomial Theorem to expand $(x+1)^3$.

Related terms

Polynomial: An algebraic expression consisting of one or more terms, each term including a variable raised to an exponent and multiplied by a coefficient.

Monomial: A single term algebraic expression that consists of a constant multiplied by one or more variables raised to non-negative integer powers.

Binomial Theorem:

A formula that provides the expanded form of $(a+b)^n$, where $n$ is a non-negative integer.