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Warm-Up #1

Warm-Up #1. Write the area of the rectangle as a product and as a sum. Warm-Up #2. Demonstrate that the product of each diagonal is equal. 8.1.2 Is there a shortcut?. Factoring with Generic Rectangles Goal : F actor a quadratic. Standard : A‑SSE.3a. Factor a

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Warm-Up #1

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  1. Warm-Up #1 • Write the area of the rectangle as a product and as a sum.

  2. Warm-Up #2 • Demonstrate that the product of each diagonal is equal.

  3. 8.1.2 Is there a shortcut? Factoring with Generic Rectangles Goal: Factor a quadratic. Standard: A‑SSE.3a. Factor a quadratic expression to reveal the zeros of the function it defines.

  4. Diagonals of Generic Rectangles

  5. Factoring Quadratics Continued • Miguel wants to use a generic rectangle to factor 3x2 + 10x + 8. He knows that 3x2 and 8 go into the rectangle in the locations shown at right. Finish the rectangle by deciding how to place the 10x term. • Write the area as a product and a sum.

  6. Kelly’s Quadratic • Kelly wants to find a shortcut to factor 2x2 + 7x + 6. She knows that 2x2 and 6 go into the rectangle in the locations shown at right. She also remembers Casey’s pattern for diagonals. Without actually factoring yet, what do you know about the missing two parts of the generic rectangle?

  7. Kelly’s Quadratic Continued • To complete Kelly’s generic rectangle, you need two x-terms that have a sum of 7x and a product of 12x2. Create and solve a Diamond Problem that represents this situation. • Use your results to complete the generic rectangle, and then write the area as a product of factors.

  8. Factor the Quadratic. 1. 2x2 + 9x + 9

  9. Factor the Quadratic. 2. x2 + 8x + 15

  10. Factor the Quadratic. 3. x2- x - 42

  11. Factor the Quadratic. 4. 4x2 - 8x + 3

  12. Factor the Quadratic. 5. 3x2 + 5x - 3

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