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8.1 + AND - POLYNOMIALS:

Monomial: a real number, a variable, or a product of both. Ex: 4, 4x, 18, -4x 2 , c, . 8.1 + AND - POLYNOMIALS:. Degree of monomial: The sum of the exponents of its variables. Ex: 4  Degree 0 4x  Degree 1 -4x 2  Degree of 2

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8.1 + AND - POLYNOMIALS:

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  1. Monomial: a real number, a variable, or a product of both. Ex: 4, 4x, 18, -4x2, c, 8.1 + AND - POLYNOMIALS: Degree of monomial: The sum of the exponents of its variables. Ex: 4  Degree 0 4x Degree 1 -4x2 Degree of 2 6x3y2 Degree of 5

  2. Polynomial: a monomial or a sum of monomials. Ex: 4 + C, 4x - 18, -4x2 + c - Standard Form of a Polynomial: Polynomials written in descending order according to their degree Ex: 1) -4x2 + 5x - 4 2) 5x3 + 11x + 6 3) 6y5 + 7y3 - 3y+ 8

  3. Degree of Polynomial in one variable: The same as the degree of the monomial with the highest degree. Ex: 1) -4x2 + 5x - 4  Degree 2 2) 5x3 + 11x + 6  Degree 3 3) 6y5+ 7y3 - 3y+ 8  Degree 5

  4. GOAL:

  5. To classify a polynomial we look at the degree and the number of terms (monomials) it contains: CLASSIFY: 0 Monomial Constant 6 1 1 5x + 9 Binomial Linear 2 4x2+7x+ 6 2 Trinomial Quadratic 3 7x3 3 Monomial Cubic 1 3x4-4x-2 4 Trinomial Fourth Degree 3

  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) 3x2 + 5x2 - 3 2) 2x4- 5x2 + 3x2 – 7x + x 3) 4x – 1 + 5x3+ 7x – x3

  7. SIMPLIFYING POLYNOMIALS: To classify a polynomial we must simplify by adding and/or subtracting like terms:  8x2 - 3 1) 3x2 + 5x2- 3  Quadratic Binomial 2) 2x4- 5x2 + 3x2– 7x + x  2x4– 2x2 – 6x  Fourth Degree Trinomial 3) 4x – 1 + 5x3+ 7x – x3  4x3+ 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 = – 7.1x2– 180x + 5800 Backgcountry = 21x2 – 140x + 1900 What is the total number of stays?

  9. Solution: We can add/subtract polynomials by adding like terms: Campground  – 7.1x2– 180x + 5800 Backgcountry  21x2 – 140x + 1900 13.9x2 – 320x + 7700 Total stays:  13.9x2 – 320x + 7700

  10. SUBTRACTION: We must not forget to distribute then add/subtract: (x3 – 3x2+5x) – (7x3+5x2 – 12) x3– 3x2 + 5x – 7x3–5x2+ 12 – 6x3– 8x2 +5x + 12 Classify: Cubic 4th term polynomial

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

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

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