Objective: Identify the name and degree of a polynomial, write polynomials in descending order, and evaluate polynomials.
In an algebraic expression, a term is a number, a variable, or a product or quotient of numbers and/or variables. A monomial is a term that does not include division by a variable; in other words, a monomial is an expression having the form axn, in which a is a constant and n is a positive integer.
A polynomial is a monomial or a sum of monomials. A polynomial composed of two terms is called a binomial, while a polynomial composed of three terms is called a trinomial. In any polynomial, the constant of a term is called the coefficient, and the degree of a term is the number of variable factors in that term. Polynomials are most commonly written in descending order, with the term having the highest degree appearing first, followed by the term of next highest degree, and so on until the term of lowest degree is last. The degree of the polynomial is the same as the degree of the term having the highest degree.
Watch the video below to see some examples of how these words and concepts are used to describe polynomials.
To simplify a polynomial means to combine all of the like terms, which are terms containing the same variable factors, and write the polynomial in descending order. To evaluate a polynomial means to find the numerical value of the expression when each variable in the polynomial is replaced by a given number. When evaluating a polynomial, it is important to follow the rules for order of operations in a mathematical expression. Watch the video below to see some examples.
Complete the worksheet attachment below and then check your answers using the solutions attachment. Once you have completed these exercises, click the link to advance to the next lesson.