Skip to ContentGo to accessibility pageKeyboard shortcuts menu
OpenStax Logo
Algebra 1

6.3.6 Practice

Algebra 16.3.6 Practice
Search for key terms or text.

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

Double click on mathematical expressions/equations to enlarge.


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
  1. ( 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.
  1. ( 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
  1. ( 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.
  1. ( 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
  1. ( 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
  1. Find ( f g ) ( x ) .
  1. x − 9
  2. x − 3
  3. x − 12
  4. x + 9
  1. Find ( f g ) ( − 1 ) .
  1. 8
  2. − 4
  3. − 10
  4. − 8
  1. 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
  1. 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
PreviousNext
Citation/Attribution

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution-NonCommercial-ShareAlike License and you must attribute OpenStax.

Attribution information
  • If you are redistributing all or part of this book in a print format, then you must include on every physical page the following attribution:

    Access for free at https://openstax.org/books/algebra-1/pages/about-this-course

  • If you are redistributing all or part of this book in a digital format, then you must include on every digital page view the following attribution:

    Access for free at https://openstax.org/books/algebra-1/pages/about-this-course

Citation information

© May 21, 2025 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.