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Practice

9.4.6 Practice

9.4.6 • Practice

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

  1. Select three expressions that are perfect squares.
  1. 9 x 2 + 24 x + 16
  2. 2 x 2 + 20 x + 100
  3. ( 7 − 3 x ) 2
  4. ( 5 x + 4 ) ( 5 x − 4 )
  5. ( 1 − 2 x ) ( − 2 x + 1 )
  6. 4 x 2 + 6 x + 94
  1. Find the missing number that makes the expression a perfect square.
49 x 2 − _ _ _ _ _ _ x + 16
36 x 2 + _ _ _ _ _ _ x + 4
4 x 2 − _ _ _ _ _ _ x + 25
9 x 2 + _ _ _ _ _ _ x + 9
121 x 2 + _ _ _ _ _ _ x + 9
  1. Choose the completely factored form of the expression.
  1. 49 x 2 − 56 x + 16
  1. ( 28 x − 11 ) 2
  2. ( 7 x − 4 ) 2
  3. ( 49 x − 16 ) 2
  4. ( 7 x + 4 ) 2
  1. 36 x 2 + 24 x + 4
  1. 4 ( 3 x + 1 ) 2
  2. ( 6 x + 2 ) 2
  3. ( 36 x + 4 ) 2
  4. ( 6 x − 2 ) 2
  1. 4 x 2 − 20 x + 25
  1. ( 2 x + 5 ) 2
  2. ( 4 x − 25 ) 2
  3. ( 2 x − 5 ) 2
  4. ( 10 x + 7 ) 2
  1. 121 x 2 + 66 x + 9
  1. ( 11 x − 3 ) 2
  2. ( 3 x − 3 ) 2
  3. ( 121 x − 9 ) 2
  4. ( 11 x + 3 ) 2
  1. Find the missing number that makes the expression a perfect square.
9 x 2 + 42 x + _ _ _ _ _
49 x 2 − 28 x + _ _ _ _ _
25 x 2 + 110 x + _ _ _ _ _
64 x 2 − 144 x + _ _ _ _ _
4 x 2 + 24 x + _ _ _ _ _
  1. Based on your responses in question 4 above, choose the factored form of the expression.
  1. 9 x 2 + 42 x + _ _ _ _ _
  1. ( 9 x + 3 ) 2
  2. ( 3 x − 7 ) 2
  3. ( 9 x − 21 ) 2
  4. ( 3 x + 7 ) 2
  1. 49 x 2 − 28 x + _ _ _ _ _
  1. ( 7 x + 7 ) 2
  2. ( 7 x − 2 ) 2
  3. ( 7 x + 2 ) 2
  4. ( 4 x + 7 ) 2
  1. 25 x 2 + 110 x + _ _ _ _ _
  1. ( 5 x + 11 ) 2
  2. ( 11 x − 5 ) 2
  3. ( 11 x + 5 ) 2
  4. ( 5 x − 11 ) 2
  1. 64 x 2 − 144 x + _ _ _ _ _
  1. ( 8 x + 9 ) 2
  2. ( 64 x − 9 ) 2
  3. ( 8 x − 9 ) 2
  4. ( 72 x − 17 ) 2
  1. 4 x 2 + 24 x + _ _ _ _ _
  1. ( x + 6 ) 2
  2. ( 2 x + 6 ) 2
  3. ( 4 x − 26 ) 2
  4. ( 2 x − 6 ) 2
  1. For each expression, find the value of c to make a perfect square in standard form ( a x 2 + b x + c ) .
4 x 2 + 4 x + c
25 x 2 − 30 x + c
  1. Use the value of c needed to make the expression a perfect square (from the previous question). Then, solve each equation.
  1. 4 x 2 + 4 x + c = 0
  1. x = 1 6
  2. x = 2
  3. x = − 3 2
  4. x = 3 2
  5. x = − 1 2
  6. x = 1 2
  1. 25 x 2 − 30 x + c = 0
  1. x = 3 5
  2. x = 5
  3. x = 4
  4. x = 2 5
  5. x = − 4 5
  6. x = 1 2