
Algebra is a branch of mathematics. In algebra, letters are used to represent numbers. Literal: The letters used to represent numbers are called literal numbers or literals. Variable: In algebra, the letter that stands for an unknown number is called a variable. The variables in 8x^{2}y^{3} are x and y. Numeric Coefficient: The number that multiplies a variable or variables is called a coefficient. It is usually written in front of the variable or variables. The coefficient in 9yz^{4} is 9. When the coefficient is 1, it is typically not written (i.e., 1yz^{4} = yz^{4} and 1a^{3} = a^{3}). Exponent/Index and Base: The power to which a variable is raised is called an exponent. The number or variable that is multiplied by itself is called the base. In 7a^{5}, the exponent is 5 and the base is a. When the exponent is 1, it is typically not written (i.e., 6y^{1}z^{4} = 6yz^{4}). Any variable or a number raised to the power zero gives one (i.e., x^{0} = 1). Term: A term is a number, variable, or the product of a number and variable(s). Examples of terms are 3x, 4x^{3}, 7xy, x.
Like Terms are terms that have the exact same variables raised to the exact same exponents.
Algebraic Expression: An algebraic expression is one or more algebraic terms in a phrase. It can include variables, constants, and operating symbols, such as plus and minus signs. It is only a phrase, not the whole sentence, so it doesn't include an equal sign. In an algebraic expression, terms are the elements separated by plus or minus signs. The above example has four terms, 2x^{2}, 4y, 8xy, and 15. Terms may consist of variables and coefficients, or constants.
Algebraic Equation: An equation is a statement that two numbers or expressions are equal. Algebraic Inequalities: An algebraic inequality is a mathematical statement comparing two unequal algebraic expressions. It states that one algebraic expression is greater than (>), less than (<), greater than or equal to (>=), or less than or equal to (<=) another algebraic expression.
Monomial: Any number or a variable or a product of numbers and variables is called a monomial. Each of the following is an example of a monomial:
Polynomial: An expression containing a finite sum of terms.
The following are NOT Polynomials:
Binomial: A polynomial with two terms.
Trinomial: A polynomial with three terms. Degree of a Term: The degree of a term is the sum of the exponents on the variables contained in the term. For example, the degree of the term 4x^{2} is 2.
Degree of a Polynomial: The degree of a polynomial is the largest degree of all its terms. Directions: Answer the following questions. Also write at least 5 examples of each of the above terms. 