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Module 1 Algebra Factoring Trinomial Expressions.

Module 1 Algebra Factoring Trinomial Expressions. Review. You have learned about factoring expressions using the Greatest Common Factor (gcf). You have learned about solving equations using the Zero Product Rule. Bellringer: Solve 2x 2 – 10x = 0. Review (cont’d).

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Module 1 Algebra Factoring Trinomial Expressions.

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  1. Module 1AlgebraFactoring Trinomial Expressions.

  2. Review You have learned about factoring expressions using the Greatest Common Factor (gcf). You have learned about solving equations using the Zero Product Rule. Bellringer: Solve 2x2 – 10x = 0

  3. Review (cont’d) You have also learned about using the box method to multiply algebraic expressions: try: (x+1)(x+4). Factor: a number or quantity that when multiplied with another produces a given number or expression. We will now learn about how to factor a trinomial such as x2 + 5x + 4.

  4. CCSS Learning Outcomes

  5. INTRODUCTION • Algebra tiles can be used to model factoring algebraic expressions . • There are three types of tiles: 1. Large square with x as its length and width. 2. Rectangle with x and 1 as its length and its width 3. Small square with 1 as its length and width. x 1 1 x 1 x

  6. INTRODUCTION • Each tile represents an area. x Area of large square = x (x) = x2 x 1 x Area of rectangle = 1 (x) = x 1 1 Area of small square = 1 (1) = 1

  7. ALGEBRAIC EXPRESSIONS • To model x2 + 5x + 4, you need 1 x2 tile, 5 x tiles and 4 one tiles. x2 x x x x x The object is to place these in your grid and form a rectangle. The lengths of each tile must match with the other tiles in its row or column.

  8. Algebra Tiles Factor: x2 + 5x + 4

  9. What is the length of the rectangle? What is the width of the rectangle?

  10. Now fill in factors: X + 1 X + 4 Therefore, the factored form of x2 + 5x + 4 = (x+1)(x+4)

  11. How would you check your answer? (hint: Check review slide.) x2 + 5x + 4 = (x+1)(x+4)

  12. Factor: x2 + 3x + 2 • To model x2 + 3x + 2, you need 1 x2 tile, 3 x tiles and 2 one tiles. x2 x x x

  13. Factor: x2 + 3x + 2 • Algebra Tiles

  14. What is the length of the rectangle? What is the width of the rectangle?

  15. Now fill in factors: X + 1 X + 2 Therefore, the factored form of x2 + 3x + 2 = (x+1)(x+2)

  16. How would you check your answer? x2 + 3x + 2 = (x+1)(x+2)

  17. Are you ready? Working in Partners: Factor: x2 + 7x + 6 using Algebra Tiles When complete, write your final answer in factored form on your wipe board.

  18. Let’s factor 2x2 + 5x + 2. You need 2 x2 tile, 5 x tiles and 2 one tiles. x2 x2 x x x x x 1 1

  19. Algebra Tiles 2x2 + 5x + 2

  20. Now fill in factors: X + 2 2X + 1 Therefore, the factored form of 2x2 + 5x + 2 = (2x+1)(x+2)

  21. How about… Factoring 2x2 + 7x + 3 using Algebra Tiles When complete, write your final answer in factored form on your wipe board.

  22. Lesson Wrap-Up In this lesson, you learned how to factor trinomials using Algebra Tiles. You visually saw the connection between the area of a rectangle and its length and width, each represented by algebraic expressions (polynomials).

  23. Here’s more: x2 + 9x + 8 2x2 + 9x + 9 x2 + 8x + 16 2x2 + 10x + 8

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