Section 5.4 Adding and Subtracting Polynomials

5.4 Lecture Guide: Adding and Subtracting Polynomials Objective: Use the terminology associated with polynomials.

Monomials and Polynomials: Monomials Verbally A monomial is a real number, a variable, or a product of real numbers and variables with whole number exponents. Algebraic Examples x, A, and are monomials. Verbally Algebraic Examples Polynomials A polynomial is a monomial or a sum of monomials. and are polynomials. is a polynomial.

Monomials and Polynomials: Verbally Algebraic Examples Binomial A binomial is a polynomial containing two terms. Verbally Algebraic Examples Trinomial A trinomial is a polynomial containing three terms.

1. Determine whether each expression is a polynomial. Classify each polynomial according to the number of terms it contains. (a) Polynomial? Yes / No Classification: ____________

(b) Polynomial? Yes / No Classification: ____________ 1. Determine whether each expression is a polynomial. Classify each polynomial according to the number of terms it contains.

(c) Polynomial? Yes / No Classification: ____________ 1. Determine whether each expression is a polynomial. Classify each polynomial according to the number of terms it contains.

(d) Polynomial? Yes / No Classification: ____________ 1. Determine whether each expression is a polynomial. Classify each polynomial according to the number of terms it contains.

Degree of a Monomial: The degree of a monomial is the sum of the exponents for all the variables in this term. A nonzero constant is understood to have degree zero with exponent but no degree is assigned to the monomial Determine the coefficient and the degree of each monomial. (a) Coefficient: ______ Degree: ______ (b) Coefficient: ______ Degree: ______

2. Determine the coefficient and the degree of each monomial. (c) Coefficient: ______ Degree: ______ (d) Coefficient: ______ Degree: ______ x

Standard Form of a Polynomial: A polynomial is in standard form if (1) the variables in each term are written in alphabetical order and (2) the terms are arranged in descending powers of the first variable. Degree of a Polynomial: The degree of a polynomial is the same as the degree of the term with the highest degree. To find this highest degree, examine each term individually---do not sum the degrees of the terms.

3. Write each polynomial in standard form, and give the degree of each polynomial. (a) Standard form: Degree:

3. Write each polynomial in standard form, and give the degree of each polynomial. (b) Standard form: Degree:

3. Write each polynomial in standard form, and give the degree of each polynomial. (c) Standard form: Degree:

4. The profit in dollars made by selling x units is given by the polynomial (a) Evaluate Evaluate and interpret each expression. Interpret

4. The profit in dollars made by selling x units is given by the polynomial (b) Evaluate Evaluate and interpret each expression. Interpret

4. The profit in dollars made by selling x units is given by the polynomial (c) Evaluate Evaluate and interpret each expression. Interpret

Objective: Add and subtract polynomials. When adding or subtracting polynomials, remember to use the __________________ property to remove any grouping symbols and then add like terms. Remember that like terms have exactly the same variable factors.

Identify each pair of terms as like or unlike. 5.and

Identify each pair of terms as like or unlike. 6.and

Determine the sum or difference and write the result in standard form. 7.

Determine the sum or difference and write the result in standard form. 8.

Determine the sum or difference and write the result in standard form. 9.

Determine the sum or difference and write the result in standard form. 10.

Determine the sum or difference and write the result in standard form. 11.

Determine the sum or difference and write the result in standard form. 12.

Determine the sum or difference and write the result in standard form. 13.

Determine the sum or difference and write the result in standard form. 14.