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Algebra 1

6.3.6 Practice

Algebra 16.3.6 Practice
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Complete the following questions to practice the skills you have learned in this lesson.


For questions 1 - 2, find the quotients using division.

1. 45 x 5 y 9 − 60 x 8 y 6
  1. − 3 4 x 3 y 3
  2. − 3 y 3 4 x 3
  3. − 4 y 3 3 x 3
  4. − 3 x 3 4 y 3
2. ( 48 y − 24 x ) ÷ ( 2 y − x )
  1. − 24
  2. 24 y
  3. − 24 x
  4. 24
For questions 3 and 4, divide using long division.
3. ( m 3 + 1000 ) ÷ ( m + 10 )
  1. m 2 − 10 m + 100
  2. m 2 + 10 m − 100
  3. m 2 − 100
  4. m 2 + 10 m
4. ( 125 y 3 − 64 ) ÷ ( 5 y + 4 )
  1. 25 y 2 − 20 y + 16
  2. 25 y 2 + 20 y + 16
  3. 25 y 2 − 20 y + 16 − 64 5 y + 4
  4. 25 y 2 − 20 y + 16 − 128 5 y + 4
For questions 5 - 6, divide using synthetic division.
5. ( b 3 − 3 b 2 − 4 b + 12 ) ÷ ( b + 2 )
  1. b 2 + 5 b − 6 ; remainder 0
  2. b 2 − 5 b ; remainder 6
  3. b 2 − 5 b + 6 ; remainder 0
  4. b 2 + 5 b ; remainder 6
6. ( 3 x 4 − 11 x 3 + 2 x 2 + 10 x + 6 ) ÷ ( x − 3 )
  1. 3 x 3 − 2 x 2 − 4 x ; remainder − 2
  2. 3 x 3 − 2 x 2 − 4 x − 2 ; remainder 0
  3. 3 x 3 − 20 x 2 − 62 x − 180 ; remainder 0
  4. 3 x 3 + 2 x 2 + 4 x + 2 ; remainder 0

For questions 7 and 8, use the following polynomial functions.

  • f ( x ) = x 2 − 13 x + 36
  • g ( x ) = x − 4
7. Find ( f g ) ( x ) .
  1. x − 9
  2. x − 3
  3. x − 12
  4. x + 9
8. Find ( f g ) ( − 1 ) .
  1. 8
  2. − 4
  3. − 10
  4. − 8
9. Use the Remainder Theorem to find the remainder.

f ( x ) = x 2 − 4 x − 9 is divided by x + 2

  1. -9
  2. -13
  3. 21
  4. 3
10. Use the Factor Theorem to determine if x − 3 is a factor of x 3 − 7 x 2 + 11 x + 3 .
  1. No
  2. Yes
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