1. 8.1 + AND - POLYNOMIALS: Monomial: a real number, a variable, or a product of both. Degree of monomial: The sum of the exponents of its variables. Ex: 4  Degree 0 4x  Degree 1 -4x 2  Degree of 2 6x 3 y 2  Degree of 5

2. Polynomial: a monomial or a sum of monomials. Standard Form of a Polynomial: Polynomials written in descending order according to their degree Ex: 1) -4x 2 + 5x - 4 2) 5x 3 + 11x + 6 3) 6y 5 + 7y 3 - 3y + 8

3. Degree of Polynomial in one variable: The same as the degree of the monomial with the highest degree. Ex: 1) -4x 2 + 5x - 4  Degree 2 2) 5x 3 + 11x + 6  Degree 3 3) 6y 5 + 7y 3 - 3y + 8  Degree 5

4. GOAL:

5. CLASSIFY: To classify a polynomial we look at the degree and the number of terms (monomials) it contains: PolynomialDegreeName Using Degree Number of Terms Name Using number of Terms 6 0 Constant 1 Monomial 5x + 91 Linear 2 Binomial 4x 2 +7x+ 62 Quadratic 3 Trinomial 7x 3 3 Cubic 1 Monomial 3x 4 -4x-24 Fourth Degree3 Trinomial

6. CLASSIFY: To classify a polynomial we must simplify. SIMPLIFYING POLYNOMIALS: To classify a polynomial we must simplify by adding and/or subtracting like terms: Ex: Classify the following polynomials: 1) 3x 2 + 5x 2 - 3 2) 2x 4 - 5x 2 + 3x 2 – 7x + x 3) 4x – 1 + 5x 3 + 7x – x 3

7. SIMPLIFYING POLYNOMIALS: To classify a polynomial we must simplify by adding and/or subtracting like terms: 1) 3x 2 + 5x 2 - 3 2) 2x 4 - 5x 2 + 3x 2 – 7x + x 3) 4x – 1 + 5x 3 + 7x – x 3  8x 2 - 3  Quadratic Binomial  2x 4 – 2x 2 – 6x  Fourth Degree Trinomial  4x 3 + 11x – 1  Cubic Trinomial Notice: Must put in standard form before classifying!

8. REAL-WORLD (ADDITION): We can add/subtract polynomials by adding like terms: Ex:A researcher studied the number of overnight stays in the US National Park Service campgrounds and in the backcountry of the national park system over a 5-yr period. He model his results as following: Campground = – 7.1x 2 – 180x + 5800 Backgcountry = 21x 2 – 140x + 1900 What is the total number of stays?

9. Solution: We can add/subtract polynomials by adding like terms: Campground  – 7.1x 2 – 180x + 5800 13.9x 2 – 320x + 7700 Backgcountry  21x 2 – 140x + 1900 Total stays:  13.9x 2 – 320x + 7700

10. SUBTRACTION: We must not forget to distribute then add/subtract: (x 3 – 3x 2 +5x) – (7x 3 +5x 2 – 12) x 3 – 3x 2 + 5x – 7x 3 – 5x 2 + 12 – 6x 3 – 8x 2 +5x + 12 Classify: Cubic 4 th term polynomial

11. VIDEOS: Polynomials Adding and Subtracting Polynomials: https://www.khanacademy.org/math/trigonometry/polyn omial_and_rational/polynomial_tutorial/v/addition-and- subtraction-of-polynomials

12. CLASSWORK: Page 477-479: Problems: As much as needed to master the concept