Algebra Homework Help : Algebraic Terms and Definitions

What are Some of the Commonly Used Terms in Algebra?

In algebra, the letter that stands for an unknown number is called a variable. The variables in 8x²y³ are x and y.

The number that multiplies a variable or variables is called the coefficient. It is usually written in front of the variable or variables. The coefficient in 9yz⁴ is 9. When the coefficient is 1, it is typically not written (i.e., 1yz⁴ = yz⁴ and 1a³ = a³).

The power to which a variable is raised is called the exponent. The exponent in 7a⁵ is 5. When the exponent is 1, it is typically not written (i.e., 6y¹z⁴ = 6yz⁴). Any variable or number raised to the power zero gives one (i.e., x⁰ = 1).

Any number or variable or product of numbers and variables is called a monomial. Each of the following is an example of a monomial :
5, −7, x, y, 6xyz, −9yz⁴, 2.3a³

A monomial or the sum of two or more monomials is called a polynomial. Each of the following is an example of a polynomial :
6xyz, 5a³ − 21, 4x² − 9y², 2x + 3y + 4z, 5x² + 6x + 7

Each monomial that makes up a polynomial is referred to as a term of the polynomial.

A polynomial that has two (unlike) terms is called a binomial (e.g., 6a³ − 23 and 5x² + 18y²).

A polynomial that has three (unlike) terms is called a trinomial. (e.g., 3x + 5y + 7z and 6x² + 9x + 12).

Like terms are those that have exactly the same variables and exponents. They may differ only in their coefficients. Importantly, the only algebraic terms that can be combined (added or subtracted) are like terms. Thus, 7y²z and −9y²z are like terms, but x²y and xy² are unlike terms.

A collection of algebraic terms connected by mathematical symbols is called an algebraic expression, and an algebraic expression whose parts are not separated by + or − signs is called a term. Thus, 5x² + 3xy + 2y² is an algebraic expression with three terms 5x², 3xy and 2y².

A statement that two algebraic expressions are equal is called an equation. Each of the following is an example of an equation :
2x + 7 = 5x − 8
x² + 5x + 6 = 0

An equation where the highest power to which a variable is raised is one is called a linear equation. Thus, 3x − 7 = 7x + 3 is an example of a linear equation.

An equation where the highest power to which a variable is raised is two is called a quadratic equation. Thus 3x² + 6x + 10 = 0 is an example of a quadratic equation.

An equation where the highest power to which a variable is raised is three is called a cubic equation. Thus 7x³ + 8x + 9 = 0 is an example of a cubic equation.

An equation where the highest power to which a variable is raised is four is called a quartic equation. Thus 7x⁴ + 15x³ + 8x² + 9 = 0 is an example of a quartic equation.

Practice Exercise for Algebra Module on Algebraic Terms & Definitions

Practice Exercise for Algebra Module on Algebraic Terms & Examples