Warm Up Simplify the expression 1.) 3x 2 – 4x – 2x 2 – 5x 2.) -2d d ) 3(2r + 4r 2 – 7r + 4r 2 )

8.1 Adding and Subtracting Polynomials

Objective Classify, add, and subtract polynomials

Monomials A monomial is a real number, a variable, or a product of a real number and one or more variables with whole-number exponents. Ex: 18, z, -4x 2, 2.5xy 3 A degree of a monomial is the sum of the exponents of its variables. The degree of a nonzero constant is 0. Zero has no degree.

Example 1 – Finding the Degree of a Monomial What is the degree of the monomial? 1.) 8x 2.) 4x 2 y 5 3.) 7

Example 2 – Adding and Subtracting Monomials What is the sum or difference? 1.) 2x 2 + 7x 2 2.) 8x 2 y – 3x 2 y

Polynomials A polynomial is a sum of monomials. Ex: 3x 4 + 5x 2 – 7x + 1 When the degrees of monomial terms decrease from left to right the polynomial is said to be in standard form. The degree of a polynomial in one variable is the degree of the monomial with the greatest exponent.

Naming polynomials PolynomialDegreeName Using Degree Number of Terms Name Using Number of Terms 60Constant1Monomial 5x + 91Linear2Binomial 4x 2 + 7x + 33Quadratic3Trinomial 2x 3 3Cubic1Monomial 8x 4 – 2x 3 + 3x4Fourth Degree 3Trinomial

Example 3 – Classifying Polynomials Write each polynomial in standard form. What is the name of the polynomial based on its degree and number of terms? 1.) 6x + 2x 2 2.) 2 – 3x 2 + x 2 – 4x 3

Example 4 – Adding Polynomials The revenue generated by a company and the cost of producing x units can be modeled by the polynomials below. Revenue: 2x 2 – 120x Cost: -0.5x 2 – 300x – 8000 Add the functions to determine the net profit or loss polynomial.

Example 5 – Subtracting Polynomials What is the simplified form of (2x 3 + 4x 2 – 3x) – (6x 3 + 5x 2 – 4)?

Assignment Pg. 477 – 478 (8 – 40 even)