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Do Now. Simplify the expression. Unit 5: Polynomials. Day 01: Classifying Polynomials. Homework. Need Help? Textbook: Section 6.1: Polynomial Functions Homework Worksheet on simplifying polynomials . Objective. To classify polynomials by their degree and number of terms

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  1. Do Now • Simplify the expression

  2. Unit 5: Polynomials Day 01: Classifying Polynomials

  3. Homework • Need Help? • Textbook: Section 6.1: Polynomial Functions • Homework • Worksheet on simplifying polynomials

  4. Objective • To classify polynomials by their degree and number of terms • To simplify polynomial expressions using: • Addition • Subtraction • Multiplication

  5. Polynomials • What is a polynomial? • A mathematical expression made up of many terms. • What is a term? • A constant: 5, 8, -3 • A variable: x, y2, a4 • Or, the product of constants and variables: 5x, 7a2b3 • Terms are usually separated by addition or subtraction signs • Example of Polynomial: • 5x4 – 9x3 + 3

  6. Polynomials • Degree of a term: • The exponent of the variable • Example: 6x3 : degree of 3 • Standard Form of a Polynomial: • A polynomial with terms in descending order of exponents • Only applies to polynomials with one variable • Example: 2x4 – 7x2 + x + 14 • Leading Term • The term with the highest degree • Example: 2x4 – 7x2 + x + 14 • Leading Coefficient • The coefficient of the leading term • Example: 2x4 – 7x2 + x + 14

  7. Polynomials • Classifying Polynomials • Write in standard form • Degree (largest exponent) • # of Terms (separated by +/- signs) • Example: 2x5 +7x3 • Degree: 5 • Terms: 2

  8. Classify the Polynomials • Write each polynomial in standard form, then classify. Quintic Trinomial 7th degree Binomial Constant Monomial Quartic Polynomial of 4 terms

  9. Simplifying Polynomials • Combine Like Terms • Addition * “Like Terms” have the same constant/exponent combinations Quadratic Binomial 6th degree Trinomial * Since addition does not change any signs, remove the parentheses and CLT Cubic Polynomial of 4 terms Quadratic Binomial

  10. Simplifying Polynomials • Subtraction • Distribution * Change the sign of the terms in any polynomial after a subtraction sign. Then, remove the parentheses and CLT Cubic Polynomial of 4 terms Linear Monomial *Distribute. It is possible to multiply unlike terms. Remember to add exponents when multiplying 9th Degree Polynomial of 4 terms Quintic Trinomial

  11. Simplifying Polynomials • Multiplication * Distribute each term in the 1st set of parentheses tothe second., then CLT + Cubic Polynomial of 4 terms Cubic Polynomial of 4 terms

  12. Simplifying Polynomials • Multiplication * Distribute each term in the 1st set of parentheses with the second, then CLT + Quartic Polynomial of 5 terms Quartic Polynomial of 5 terms

  13. Did you meet today’s objectives? • Name the two properties that classify polynomials? • Which mathematical operations allow you to combine unlike terms? Which do not?

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