Chapter 8: Polynomials and Factoring Section 8.1: Adding and Subtracting Polynomials

Section 8.1: Adding and Subtracting Polynomials Goal: To classify, add, and subtract polynomials

Section 8.1: Adding and Subtracting Polynomials Monomial: a real number, a variable, or a product of a real number and one or more variables Ex: 2 -4x 3xy ½ x2 Degree of a monomial: the sum of the exponents of its variables The degree of a nonzero constant is 0 Zero has no degree Ex: 8x is a degree 1 since the x has a power of 1 4x3y2 has a degree 5 since the sum of the exponents is 5

Section 8.1: Adding and Subtracting Polynomials You try: What is the degree of the monomial? A) -3x B) 9x2y5 C) 7

Section 8.1: Adding and Subtracting Polynomials Polynomial: an expression which is the sum of terms in the form axk k is a nonnegative integer Standard form: terms are placed in descending order largest degree to smallest degree Degree of a polynomial: the same as the monomial with the highest degree

Section 8.1: Adding and Subtracting Polynomials Naming a polynomial

Section 8.1: Adding and Subtracting Polynomials Example: Write each polynomial in standard form. What is the name of the polynomial based on its degree and number of terms? A) 6x + 2x2 B) 2 + 3x2 – 4x3

Section 8.1: Adding and Subtracting Polynomials Adding and Subtracting Monomials: Can only add and subtract like terms (terms with the same variables raised to the same power) Ex: -8x3y + 12x3y = 7y + 10y3 – 2y =

Section 8.1: Adding and Subtracting Polynomials You try: 3. What is the sum or difference? A) 2x2 + 7x2 B) 8x2y – 3x2y

Section 8.1: Adding and Subtracting Polynomials Adding Polynomials: Combine Like terms and place in descending order Subtracting Polynomials: Distribute a negative one into the polynomial being subtracted, combine like terms, and place in descending order

Section 8.1: Adding and Subtracting Polynomials Examples: 4. Simplify the following: A) (6x2 – x + 3) + (-2x + x2 – 7) B) (-8x3 + x – 9x2 + 2) + (8x2 – 2x + 4) + (4x2 – 1 – 3x3)

Section 8.1: Adding and Subtracting Polynomials Examples: 5. Find the difference. Write the answer in standard form A) (-6x3 + 5x – 3) – (2x3 + 4x2 – 3x + 1) B) (12x – 8x2 + 6) – (-8x2 – 3x + 4)

Section 8.1: Adding and Subtracting Polynomials Example: 6. The revenue generated by a company and the cost of producing x units can be modeled by the polynomials below. Revenue: 2x2 + 120x Cost: -0.5x2 – 300x – 8000 Add the functions to determine the net profit or loss polynomial

Section 8.1: Adding and Subtracting Polynomials Homework: Pg. 489 #8-46 (even)