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Exploring Algebra: Classifying and Multiplying Polynomials

This lesson focuses on the essential methods used in algebra for classifying and multiplying polynomials. Students will learn to identify polynomials by degree and number of terms, understand leading coefficients, and write in standard form. They will explore various multiplication techniques, including the distributive property, and apply these methods in problem-solving contexts. Additionally, fun examples and practice problems will reinforce learning and engagement.

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Exploring Algebra: Classifying and Multiplying Polynomials

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  1. 9-18-13 Warm-Up • 3x + 6x2 – 10 + 9x2 + 2x • 5x2y + 3xy – 8x2y + 6xy • (2x2)(-4x3) • 2(x + 4) • 7(12 + 3x) – 10 15x2 + 5x - 10 -3x2y + 9xy 3x2 -8x5 2x + 8 21x + 74

  2. Homework Review

  3. CCGPS AlgebraDay 30 (9-18-13) UNIT QUESTION: In what ways can algebraic methods be used in problems solving? Standard: MCC9-12.N.RN.1-3, N.CN.1-3, A.APR.1 Today’s Question: What methods can we use to multiply polynomials? Standard: MCC9-12.A.APR.1

  4. Classifying Polynomials Objective: To classify polynomials by degree and by number of terms Example of a Polynomial Degrees Constant Coefficients

  5. Vocabulary Degree:is the exponent for each variable. Degree of the polynomial: is the largest exponent of the polynomial. Leading coefficient:is the coefficient of the first term. Descending order/Standard formis how polynomials are written where the terms are placed in descending order from largest degree to smallest.

  6. Example: Write the polynomials in Standard form/descending order. Then identify the leading coefficient and degree of the polynomial. 1. Degree is 7 Leading coefficient is 3 2. Degree is 4 leading coefficient is –2

  7. Classifying Polynomials By Degree Constant 0 6 -3 Linear 1 3x + 4 -7x + 2 Quadratic 2 Cubic 3 Quartic 4

  8. Classifying polynomials By # of terms Monomial 1 3x Binomial 2 3x + 1 Trinomial 3 Note: Any polynomials with four or more terms are just called polynomials

  9. Multiplying PolynomialsMonomial x Polynomial

  10. (5)(x + 6)

  11. (x2)(x + 6)

  12. (-2x)(x2 – 4x + 2)

  13. Multiplying PolynomialsBinomial x Binomial or Trinomial

  14. F f f Ff ff f Ff ff Genetics Punnett Squares are diagrams used by scientists to help them to figure out how inherited traits (characteristics) will be distributed. We will use something like a Punnett Square today to help us learn how to multiply polynomials!!

  15. Multiplying Polynomials Using the distributive property

  16. Notes - Multiplying Polynomials F - First O - Outside I – Inside L - Last (z + 5) (z + 3)

  17. (x - 2) (x + 4)

  18. (x + 9) (x – 3)

  19. (x + 3) (x – 3)

  20. (2x + 5)(x + 6)

  21. (3x – 1)(2x – 4)

  22. (5b – 6)(3b2 – 2b + 5)

  23. Find the area of the rectangle.

  24. Find the area of the rectangle.

  25. Find the volume.

  26. Practice Why is a stick of gum like a sneeze?

  27. HomeworkPractice Worksheet

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