Add and Subtract Polynomials Quiz

PDF page 694: Monomials m A monomial is a term of the form ax , where a is a constant and m is a positive whole number.

PDF page 694: • binomial—A polynomial with exactly two terms is called a binomial.

PDF page 694: • monomial—A polynomial with exactly one term is called a monomial.

PDF page 695: The degree of a polynomial and the degree of its terms are determined by the exponents of the variable. A monomial that has no variable, just a constant, is a special case. The degree of a constant is 0—it has no variable.

PDF page 695: The degree of a term is the sum of the exponents of its variables. The degree of a constant is 0. The degree of a polynomial is the highest degree of all its terms. Let’s see how this works by looking at several polynomials. We’ll take it step by step, starting with monomials, and then progressing to polynomials with more terms.

PDF page 695: The degree of a term is the sum of the exponents of its variables. The degree of a constant is 0. The degree of a polynomial is the highest degree of all its terms. Let’s see how this works by looking at several polynomials. We’ll take it step by step, starting with monomials, and then progressing to polynomials with more terms.

PDF page 695: A polynomial is in standard form when the terms of a polynomial are written in descending order of degrees. Get in the habit of writing the term with the highest degree first.

PDF page 694: A monomial, or two or more monomials combined by addition or subtraction, is a polynomial. Some polynomials have special names, based on the number of terms. A monomial is a polynomial with exactly one term. A binomial has exactly two terms, and a trinomial has exactly three terms. There are no special names for polynomials with more than three terms.

PDF page 696: 40y Combine like terms.

PDF page 696: EXAMPLE 6.3 2 2 Add: 25y + 15y . Solution

PDF page 696: You have learned how to simplify expressions by combining like terms. Remember, like terms must have the same variables with the same exponent. Since monomials are terms, adding and subtracting monomials is the same as combining like terms. If the monomials are like terms, we just combine them by adding or subtracting the coefficient.

PDF page 697: Remember that like terms must have the same variables with the same exponents.

PDF page 696: You have learned how to simplify expressions by combining like terms. Remember, like terms must have the same variables with the same exponent. Since monomials are terms, adding and subtracting monomials is the same as combining like terms. If the monomials are like terms, we just combine them by adding or subtracting the coefficient.

PDF page 697: EXAMPLE 6.5 2 2 2 Simplify: c + 7d − 6c . Solution

PDF page 697: 2 2 Combine like terms. −5c + 7d

PDF page 697: We can think of adding and subtracting polynomials as just adding and subtracting a series of monomials. Look for the like terms—those with the same variables and the same exponent. The Commutative Property allows us to rearrange the terms to put like terms together.