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Adding, Subtracting, Multiplying, and Factoring Polynomials

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Adding, Subtracting, Multiplying, and Factoring Polynomials

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    1. One instructional strategy that will be used is deductive, Rule-Eg. I will also use Social Construction with this project because they will be working with a partner to work their way through a maze. The abduction/metaphor strategy will be used because students are starting with knowledge of adding and multiplying numbers with the same base and what to do with the exponents. One instructional strategy that will be used is deductive, Rule-Eg. I will also use Social Construction with this project because they will be working with a partner to work their way through a maze. The abduction/metaphor strategy will be used because students are starting with knowledge of adding and multiplying numbers with the same base and what to do with the exponents.

    2. Add like terms together Write in standard form Adding Polynomials Rule-Eg is used here.Rule-Eg is used here.

    3. Subtracting Polynomials Change subtraction to add the opposite Follow adding rules Rule-Eg is used here.Rule-Eg is used here.

    4. Multiplying Polynomials Use FOIL when multiplying two binomials. Use the Box Method. Rule-Eg is used here.Rule-Eg is used here.

    5. Like Terms Scaffolding is used here.Scaffolding is used here.

    9. Standard Form of a Polynomial Rule-Eg is used here.Rule-Eg is used here.

    10. Add the Opposite To add the opposite, change subtraction to addition and add the opposite of the term being subtracted. If you are subtracting a polynomial in parentheses, change everything the second parentheses to the opposite sign. Rule-Eg is used here.Rule-Eg is used here.

    11. Multiply the FIRST terms in each binomial Multiply the OUTER terms in each binomial Multiply the INNER terms in each binomial Multiply the LAST terms in each binomial Add like terms and write in standard form FOIL Method Rule-Eg is used here.Rule-Eg is used here.

    12. Box Method Draw a box. Write one factor on one side and write the other factor on the other side. Find the area of each small box. Add like terms of the small box areas, and write in standard form. Rule-Eg is used here.Rule-Eg is used here.

    13. Factoring Polynomials Click on a form to review how to factor x2+bx+c form ax2+bx+c form

    14. Find two factors of c whose sum is b. Example: To factor x2 + 7x + 12, find factors of 12 whose sum is 7: (choose one below) a. 6 and 2 b. -3 and -4 c. 3 and 4 Factoring x2 + bx + c form Scaffolding is used here.Scaffolding is used here.

    15. Oops! Nice try! You found factors of 12, but their sum is not 7. Try again!

    16. A binomial is a polynomial with two terms. Which of the following are binomials? 12x2 4x + 1 7x2 - 3x + 2 -14x4 - 2 Scaffolding is used here.Scaffolding is used here.

    19. Great job! 3 and 4 are factors of 12, and they add up to 7.

    20. Factoring x2 + bx + c form Factoring x2 + 7x + 12 Since 3 and 4 are the factors of 12, the factors of the polynomial are (x + 4) and (x + 3) So, x2 + 7x + 12 = (x + 4)(x + 3) Rule-Eg is used here.Rule-Eg is used here.

    21. Factoring ax2+bx+c form Multiply the first and last terms. Find factors of that term whose sum is bx. Example: To factor 2x2+11x+5, multiply 2x2 and 5 to get 10x2. Then find factors of 10x2 whose sum is 11x. (Click on the correct factors below.) a. 5x and 2x b. 10x and x c. -10x and -1x Scaffolding is used here.Scaffolding is used here.

    22. Oops! Nice try! You found factors of 10x2, but their sum is not 11x. Try again!

    23. Great job! 10x and x are factors of 10x2, and they add up to 11x. Go on to the next step.

    24. Factoring 2x2+11x+5 Now that you’ve found the two factors,10x and x, make a box. Put the first term of the polynomial in the first square Put the last term in the polynomial in the last square Put the two factors in the 2nd and 3rd square. Rule-Eg is used here.Rule-Eg is used here.

    25. Factoring 2x2+11x+5 Now factor out the common factor in each row and column. The factors are the sides of the box. 2x2+11x+5 = (x + 5)(2x + 1) Rule-Eg is used here.Rule-Eg is used here.

    26. Factor 3x2 + 10x + 8 Scaffolding is used here.Scaffolding is used here.

    27. You are ready to move on to the maze!

    28. a. 5x2 - 2x + 5 b. 5x2 + 8x + 5 c. 5x2 + 2x + 5

    37. Go back and try again!

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