Adding and Subtracting Polynomials Section 5.4 Adding and Subtracting Polynomials

5.4 Lecture Guide: Adding and Subtracting Polynomials Objective 1: Use the terminology associated with polynomials. Monomials Polynomials Verbally A monomial is a real number, a variable, or a product of real numbers and variables with _______________ number exponents. A polynomial is a monomial or a sum of a finite number of _______________. Algebraic Examples – 5, , x, A, 5x, 7xy and are monomials. and are polynomials. is a polynomial.

A binomial is a polynomial containing _______________ terms. Trinomial Verbally A binomial is a polynomial containing _______________ terms. A trinomial is a polynomial containing _______________ terms. Algebraic Examples

Degree of a Monomial The degree of a monomial is the sum of the _______________ for all the variables in this term. A nonzero constant is understood to have degree _______________ with exponent , but no degree is assigned to the monomial 0.

1. Determine whether each expression is a monomial. If the expression is a monomial, give its coefficient and the degree of each monomial. (a) (b) (c) (d) Monomial? Yes / No Coefficient: ______ Degree: ______

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

Standard Form of a Polynomial A polynomial is in standard form if (1) the variables in each term are written in ____________ order and (2) the terms are arranged in ____________ 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 ____________ 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:

Objective 2: 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 ________ factors.

Identify each pair of terms as like or unlike. 4. and 5. and

Determine the sum or difference and write the result in standard form. 6.

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.

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

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

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

15. Write a polynomial for the perimeter of the polygon.