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Practice

7.8.5 Practice

7.8.5 • Practice

Complete the following questions to practice the skills you have learned in this lesson.

  1. Choose the expression that best describes the diagram.

  1. ( 2 x + 5 ) ( x + 3 ) is equivalent to 30 x 2 .
  2. ( 2 x + 5 ) ( x + 3 ) is equivalent to 2 x 2 + 11 x + 15 .
  3. ( 2 x + 5 ) ( x + 3 ) is equivalent to 2 x 2 + 14 x + 23 .
  4. ( 2 x + 5 ) ( x + 3 ) is equivalent to 2 x 2 + 5 x + 8 .
In questions 2a–2d, match each expanded quadratic expression with an equivalent expression written as a product.
2a. x 2 + 12 x + 32
  1. ( x + 2 ) ( x + 3 )
  2. ( x + 8 ) ( x + 4 )
  3. ( x + 4 ) ( x + 2 )
  4. ( x + 2 ) ( x + 6 )
2b. x 2 + 5 x + 6
  1. ( x + 2 ) ( x + 3 )
  2. ( x + 8 ) ( x + 4 )
  3. ( x + 4 ) ( x + 2 )
  4. ( x + 2 ) ( x + 6 )
2c. x 2 + 6 x + 8
  1. ( x + 2 ) ( x + 3 )
  2. ( x + 8 ) ( x + 4 )
  3. ( x + 4 ) ( x + 2 )
  4. ( x + 2 ) ( x + 6 )
2d. x 2 + 8 x + 12
  1. ( x + 2 ) ( x + 3 )
  2. ( x + 8 ) ( x + 4 )
  3. ( x + 4 ) ( x + 2 )
  4. ( x + 2 ) ( x + 6 )
  1. Select three expressions that are equivalent to x 2 + 4 x .
  1. x ( x + 4 )
  2. ( x + 2 ) 2
  3. ( x + x ) ( x + 4 )
  4. ( x + 2 ) 2 − 4
  5. ( x + 4 ) x
Tyler drew a diagram to expand ( x + 5 ) ( 2 x + 3 ) .

Rectangle partitioned into 4 smaller rectangles. The top is labeled 2 x and 3. The side is labeled x and 5. Inside, the top row contains 2 x squared and 3 x. The bottom row contains 7 x and 8.

4a. Tyler’s diagram is incorrect. Choose the sentence that describes Tyler’s mistake.
  1. Tyler should have labeled the top x and 3 and the side 2 x and 5.
  2. Tyler should have labeled the top 2 x and 5 and the side x and 3.
  3. Tyler multiplied 5 and 2 and 5 and 3 instead of adding them.
  4. Tyler added 5 and 2 and 5 and 3 instead of multiplying them.
4b. What is the correct expanded form of ( x + 5 ) ( 2 x + 3 ) ?
  1. 2 x 2 + 13 x + 15
  2. 2 x 2 + 10 x + 8
  3. 30 x 2
  4. 3 x + 8