Teaching Algebra with Manipulatives

NAME ______________________________________________ DATE
Algebra Activity
(Use Algebra 1, Lesson 9-6)
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Factoring Trinomial Squares
Use x 2 , x , and 1 to represent x 2 , x, and 1, respectively.
Show: x 2 4x 4
Arrange the models to form a rectangle.
x 2 x 1 1
x x x x 1 1
x 1 1
1 1
x x
x 2
1. What do you notice about the length and width of the rectangle?
2. Give the dimensions of the final rectangle. (The dimensions are the
factors of the trinomial.)
Factor by forming rectangular regions with the models.
3. x 2 6x 9 4. 4x 2 4x 1 5. x 2 4x 3
6. x 2 2x 1 7. 2x 2 8x 8 8. x 2 8x 16
9. 9x 2 6x 1 10. 3x 2 4x 1 11. x 2 4
12. Which of the rectangular regions above formed squares?
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13. What do you call a trinomial whose representation is a square?
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14. How can you tell if a trinomial is a perfect square trinomial?
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15. Describe how to factor a perfect square trinomial by inspection.
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© Glencoe/McGraw-Hill 172 Teaching Algebra with Manipulatives