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Polynomial Classification and Equation Solving: Review and Reminders for May 26th

This review covers essential concepts in solving equations and polynomial classification. Students will be reminded about the upcoming test on solving polynomials and the due date for the rough draft of the cell phone project. Various examples will demonstrate how to classify polynomials by degree and the number of terms. Additionally, applications involving polynomials in real-world contexts, such as area and perimeter problems, will be explored. Lastly, participatory equation solving activities will encourage teamwork and engagement.

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Polynomial Classification and Equation Solving: Review and Reminders for May 26th

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  1. Review: Solving Equations Monday, May 26th

  2. Reminders • Test on solving polynomials tomorrow …questions? • Rough draft of cell phone project due Wednesday

  3. Classify the polynomial 3x4y – 4xy + y2 by degree Degree = 2 Degree = 3 Degree = 4 Degree = 5

  4. Classify the polynomial 3x4y – 4xy + y2 by degree Degree = 2 Degree = 3 Degree = 4 Degree = 5

  5. Classify the polynomial 3x4y – 4xy + y2 by number of terms Monomial Binomial Polynomial Other

  6. Classify the polynomial 3x4y – 4xy + y2 by number of terms Monomial Binomial Polynomial Other

  7. Classify the polynomial –xy + 1 by number of terms Monomial Binomial Polynomial Other

  8. Classify the polynomial –xy + 1 by number of terms Monomial Binomial Polynomial Other

  9. Classify the polynomial –xy + 1 by degree Degree = 0 Degree = 1 Degree = 2 Degree = 3

  10. Classify the polynomial –xy + 1 by degree Degree = 0 Degree = 1 Degree = 2 Degree = 3

  11. Applications If a fence around this field has a length of 36m, what is x? x + 7 2(x + 7) + 2(16 – 2x) = 36 2x + 14 + 32 – 4x = 36 46 – 2x = 36 16 – 2x 46 – 36 – 2x = 36 – 36 10 – 2x = 0 10 – 2x + 2x = 0 + 2x 10 = 2x 5 = x

  12. Applications If the area of this field is 27.5m2, what is x? Area = (base)(height) 2 5 27.5 = (4 + x)(5) 2 4 + x 55 = (4 + x)(5) 55 = 20 + 5x 55 – 20 = 20 + 5x – 20 35 = 5x 7 = x

  13. Applications If x = 7, what is the length of the hypotenuse? C2 = 52 + (4+x)2 C2 = 52 + (4+7)2 5 c C2 = 52 + (11)2 C2 = 25 + 121 4 + x C2 = 146 C = ±√146 C = 12.1 or -12.1

  14. What is the greatest common factor for 6xy2 – 12y3 + 15x3y2 ? Review: Factoring GCF = 3y2 Factor 6xy2 – 12y3 + 15x3y2 3y2(2x– 4y + 5x3)

  15. In a high jump competition, Seth’s height above the ground is given by h = –4x2 + 14x. Where does Seth land? Applications h = –4x2 + 14x 0 = –4x2 + 14x 0 = –2x(2x – 7) x = 0 and x = 3.5

  16. In your teams, solve as many as possible in 2 minutes. Every team member needs to be involved. Raise your hand when you have solved an equation, so that I can check it for you.

  17. Solve for b –7 + 2b + 4 – 5b = –2b 10b – b + 3 – 8b + 7 = –2(b – 4) –b(2b – 3) – 5 + 2b2 + b – 4b = 0 2 + 3b – 7b + 8 – 9 = 2 + 5b

  18. Solve for a 3a2 – a2 – 50 = 0 4 – ½a2 + a2 = 36 –2(a + 3)2 + 98 = 0 1 + 4(a – 7)2+ 5 – (a – 7)2 = 81 7 + 4(2a + 1)2 + 11 – 6(2a + 1)2 = 0

  19. Solve for d 10 – √d + 5√d + 6 = 2(√d – 1) √d + 3√d – 2(√d – 7) + 8 = √d – 4 –2√(d + 3) + √(d + 3) = 8 ½√(d – 1) + ½ – ¼√(d – 1) = ¾

  20. Solve for a 0 = 2a(3a – 1) 12a2 – 16a = 0 (a + 7)(2a – 9) = 0 –3a(4a + 1)(a – 9) = 0 0 = 5a3 – 45a

  21. Solve for x 30 – 4(x + 1)2 + 15 – (x + 1)2 = 0 4 – ½√x + √x – 3 = 7 – ¾√x + √x – 3 –2x(2x – 7)(x + 3) = 0 4x(3 – x) + 4x2 – 7x – 9 = 4 – (x + 1)

  22. Applications Calvin starts a business offering velociraptor rides for students during lunch at CCHS. He charges $7 for a 5 minute ride and $10 for a 10 minute ride. Over the course of a week, he fills 2 hours worth of riding time and makes $148. How many 5 minute rides did Calvin sell?

  23. Options: The computer lab is booked for you to work on your projectOr you may stay to do extra practice for tomorrow’s test

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