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Addition, subtraction, Multiplication and Division of Polynomials

Addition, subtraction, Multiplication and Division of Polynomials. Student Research Guide. Basics of Addition and subtraction of polynomials. Watch the following Video: (Video 1) https://youtu.be/ffLLmV4mZwU Complete the following definitions in your work document.

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Addition, subtraction, Multiplication and Division of Polynomials

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  1. Addition, subtraction, Multiplication and Division of Polynomials Student Research Guide

  2. Basics of Addition and subtraction of polynomials • Watch the following Video: (Video 1) https://youtu.be/ffLLmV4mZwU • Complete the following definitions in your work document.

  3. Basics of Addition and subtraction of polynomials • Define: what is a term? • What is a coefficient? • What is the exponent on the following variables? x, y, n, z? Why is it that I don’t need to show the exponent? • What is a polynomial? • On the following polynomial: 5x2 + x + 5 • What is the coefficient of the variable X? • What is the variable and its exponent on the constant term? • How do we arrange polynomials?

  4. Basics of Addition and subtraction of polynomials • Watch the following Video: (Video 2) https://youtu.be/DKC74YKJpNY • Complete the following definitions in your work document.

  5. Basics of Addition and subtraction of polynomials 7) What is simplifying a polynomial? 8) What are like terms? 9) Can you simplify the following polynomials? 4x2 + 3x – 2x + 8x - 5 – 10 +16x2 10) What steps did you follow to simplify the polynomial above?

  6. Basics of Addition and subtraction of polynomials • Watch the following Video: (Video 3) https://www.virtualnerd.com/algebra-1/polynomials-and-factoring/add-subtract/add/addition-example • Complete the following definitions in your work document.

  7. Basics of Addition and subtraction of polynomials 11) List the steps to add polynomials? 12) What do you do when the sign in front of the parenthesis is positive? 13) How do you combine like terms?

  8. Basics of Addition and subtraction of polynomials • Some times in order to keep things organized we might want to line up the polynomials, Watch the following Video: (Video 4) https://www.virtualnerd.com/algebra-1/polynomials-and-factoring/add-subtract/add/add-vertically-example • Complete the following definitions in your work document.

  9. Basics of Addition and subtraction of polynomials 14) What is a place holder? 15) Why could I want to use one?

  10. Basics of Addition and subtraction of polynomials • Watch the following Video: (Video 5) https://www.virtualnerd.com/algebra-1/polynomials-and-factoring/add-subtract/subtract/subtraction-example • Complete the following definitions in your work document.

  11. Basics of Addition and subtraction of polynomials 16) List the steps to subtract polynomials? 17) What do you do to get rid of the parenthesis that has the negative sign? 18) How is this process similar to adding polynomials? 19) How is it different?

  12. Basics of Addition and subtraction of polynomials • Watch the following Video: (Video 6) https://www.virtualnerd.com/algebra-1/polynomials-and-factoring/add-subtract/subtract/subtract-vertically-example • Complete the following definitions in your work document.

  13. Basics of Addition and subtraction of polynomials 20) What is the additive inverse of a polynomial?

  14. Basics of Addition and subtraction of polynomials • Watch the following Video: (Video 7) https://www.virtualnerd.com/algebra-1/polynomials-and-factoring/add-subtract/subtract/subtraction-word-problem • Complete the following definitions in your work document.

  15. Basics of Addition and subtraction of polynomials 21) Which one is the key word that lets you know what to do? 22) Once you find the equation what do you do?

  16. Basics of Addition and subtraction of polynomials • At this point you can send your Work document to Mr. Carruyo to the following address: acarruyo@goldencharter.org • If you don’t have an email, ask Mr. Carruyo for a flash drive. • Then complete the following Problems: • Page 1 – Problem 1 • Page 3 - Problem 2 (Part B) • Page 4 – Problems 1, 2 and 8. • Page 5 – Problems 2, 4, and 5. • Find each sum (solve them on your regular journal) • (7y2+2y-3)+(2-4y+5y2) • (4x2-2x+7)+(3x-7x2-9)

  17. Basics of Addition and subtraction of polynomials • Find each difference (solve them on your regular journal) • (6y2 + 8y4 − 5y) − (9y4 − 7y + 2y2) • (6n2 + 11n3 + 2n) − (4n − 3 + 5n2)    The total amount of toy sales T (in billions of dollars) consists of two groups: sales of video games V and sales of traditional toys R. In recent years, the sales of traditional toys and total sales could be represented by the following equations, where n is the number of years since 2010. R = 0.46n3 − 1.9n2 + 3n + 19 T = 0.45n3 − 1.85n2 + 4.4n + 22.6 • On your Journal , write an equation that represents the sales of videogames V. • Use the equation to predict the amount of video game sales in the year 2022. • If you have any questions Please ask Mr. Carruyo for clarification.

  18. Basics of Products of polynomials • Watch the following Video: (Video 8) https://www.virtualnerd.com/algebra-1/polynomials-and-factoring/multiply-divide/foil-multiplicaton/foil-binomial-multiplication-method • Complete the following definitions in your work document.

  19. Basics of Products of polynomials 1) What does Foil Stands for? • Now Watch this other video, and tell me how are they the same, and how are they different? (Video 9) https://www.virtualnerd.com/algebra-1/polynomials-and-factoring/multiply-divide/foil-multiplicaton/grid-multiplication-method 2) Now select any of the two methods and solve the following product of polynomials. SHOW YOUR WORK. • (8x + 4) (2x + 5)

  20. Basics of Products of polynomials • Watch the following Video: (Video 10 and 11) • https://www.virtualnerd.com/algebra-1/polynomials-and-factoring/multiply-divide/foil-multiplicaton/binomial-multiplication-word-problem • https://www.virtualnerd.com/algebra-1/exponents-exponential-functions/monomials-polynomials/polynomials/rectangle-area-from-monomial-polynomial-product • Complete the following definitions in your work document.

  21. Basics of Addition and subtraction of polynomials 3) Which key words let you know you had to multiply?

  22. Basics of Addition and subtraction of polynomials • Complete the following Problems: • Page 2 – Problem 2 and problem 3. • Page 3 - Problem 2 (Part A) • Page 4 – Problems 3, 4 and 7. • Page 5 – Problems 1 and 3. • Find each product. (solve them on your regular journal) • (y + 8)(y − 4) • (2x + 1)(x + 6) • (7z + 2)2 • (3c − 4)2 • (9d + 4)(9d − 4)

  23. Basics of Products of polynomials • Watch the following Video: (Video 12) • https://www.virtualnerd.com/algebra-1/polynomials-and-factoring/multiply-divide/distributive-multiplicaton/subtraction-and-multiplication-word-problem • Complete the following definitions in your work document.

  24. Basics of Addition and subtraction of polynomials • Some time we might have to multiply polynomials first and the perform another mathematical operation, like in the video you just watch. • Complete the following Problems: • Page 3 - Problem 1. • Page 4 – Problems 5 and 6. • Page 5 – Problems 6. • At this point you can send your Work document to Mr. Carruyo to the following address: acarruyo@goldencharter.org • If you don’t have an email, ask Mr. Carruyo for a flash drive.

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