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Dividing polynomials
    by a monomial

    Module 10 - Topic 4
Dividing a Monomial by a Monomial
Dividing a Monomial by a Monomial
 Apply the rules for dividing
 exponents:
Dividing a Monomial by a Monomial
 Apply the rules for dividing
 exponents:
   Like bases, subtract smaller from
   the larger exponent to get the
   new exponent and keep the same
   base.
Dividing a Monomial by a Monomial
 Apply the rules for dividing
 exponents:
   Like bases, subtract smaller from
   the larger exponent to get the
   new exponent and keep the same
   base.

   If the larger exponent is in the
   numerator, the result goes in the
   numerator.
Dividing a Monomial by a Monomial
 Apply the rules for dividing
 exponents:                            x5

   Like bases, subtract smaller from     3
   the larger exponent to get the
                                       x
   new exponent and keep the same
   base.

   If the larger exponent is in the
   numerator, the result goes in the
   numerator.
Dividing a Monomial by a Monomial
 Apply the rules for dividing
 exponents:                             x    5

   Like bases, subtract smaller from      3
   the larger exponent to get the
                                        x
   new exponent and keep the same
   base.                               =x   5− 3

   If the larger exponent is in the
   numerator, the result goes in the
   numerator.
Dividing a Monomial by a Monomial
 Apply the rules for dividing
 exponents:                             x    5

   Like bases, subtract smaller from      3
   the larger exponent to get the
                                        x
   new exponent and keep the same
   base.                               =x   5− 3

   If the larger exponent is in the
   numerator, the result goes in the        2
   numerator.                          =x
Dividing a Monomial by a Monomial
 Apply the rules for dividing
 exponents:                             x    5

   Like bases, subtract smaller from      3
   the larger exponent to get the
                                        x
   new exponent and keep the same
   base.                               =x   5− 3

   If the larger exponent is in the
   numerator, the result goes in the        2
   numerator.                          =x
   If the larger exponent is in the
   denominator, the result goes in
   the denominator.
Dividing a Monomial by a Monomial
 Apply the rules for dividing
 exponents:                             x    5
                                                   a4

   Like bases, subtract smaller from      3          9
   the larger exponent to get the
                                        x          a
   new exponent and keep the same
   base.                               =x   5− 3

   If the larger exponent is in the
   numerator, the result goes in the        2
   numerator.                          =x
   If the larger exponent is in the
   denominator, the result goes in
   the denominator.
Dividing a Monomial by a Monomial
 Apply the rules for dividing
 exponents:                             x    5
                                                       a    4

   Like bases, subtract smaller from      3              9
   the larger exponent to get the
                                        x              a
   new exponent and keep the same
   base.                               =x   5− 3           1
                                                   =       9− 4
   If the larger exponent is in the                    a
   numerator, the result goes in the        2
   numerator.                          =x
   If the larger exponent is in the
   denominator, the result goes in
   the denominator.
Dividing a Monomial by a Monomial
 Apply the rules for dividing
 exponents:                             x    5
                                                       a    4

   Like bases, subtract smaller from      3              9
   the larger exponent to get the
                                        x              a
   new exponent and keep the same
   base.                               =x   5− 3           1
                                                   =       9− 4
   If the larger exponent is in the                    a
   numerator, the result goes in the        2
   numerator.                          =x
                                                     1
   If the larger exponent is in the                = 5
   denominator, the result goes in                  a
   the denominator.
Simplify.
   5   3
 8a b
   2 7
 6a b
Simplify.
   5
 8a b  3
            Reduce the
   2 7      numerical part by
 6a b
            dividing the 8 and
            6 by 2.
Simplify.
   5
 8a b  3
                   Reduce the
   2 7             numerical part by
 6a b
                   dividing the 8 and
   4
     8a b  5   3
                   6 by 2.
       2 7
   3 6a b
Simplify.
   5
 8a b  3
                   Reduce the
   2 7             numerical part by
 6a b
                   dividing the 8 and
   4
     8a b  5   3
                   6 by 2.
       2 7
   3 6a b
                   Apply the rules for
                   dividing powers
                   with like bases.
Simplify.
   5
 8a b  3
                              Reduce the
   2 7                        numerical part by
 6a b
                              dividing the 8 and
   4
     8a b  5    3
                              6 by 2.
       2 7
   3 6a b
                              Apply the rules for
               4a   5−2
                              dividing powers
                  7− 3        with like bases.
               3b
                          3   And you are done
                     4a
                        4
                              dividing a monomial
                     3b       by a monomial.
Simplify each of the following.
       8   2             3   5
     12d f            27h jk
        10               9  9
     30d f            9h jk
Simplify each of the following.
               8    2        3   5
       12d f              27h jk
          10                 9  9
       30d f              9h jk

       2           2 −1
           12 f
   =            10 − 8
       5   30 d
Simplify each of the following.
               8    2        3   5
       12d f              27h jk
          10                 9  9
       30d f              9h jk

       2           2 −1
           12 f
   =            10 − 8
       5   30 d

    2f
   = 2
    5d
Simplify each of the following.
               8    2                   3     5
       12d f                      27h jk
          10                         9  9
       30d f                      9h jk

       2                           3
           12 f    2 −1
                                       27 j
   =            10 − 8
                          =            9− 3        9−5
       5   30 d               1   9h          jk

    2f
   = 2
    5d
Simplify each of the following.
               8    2                   3     5
       12d f                      27h jk
          10                         9  9
       30d f                      9h jk

       2                           3
           12 f    2 −1
                                       27 j
   =            10 − 8
                          =            9− 3        9−5
       5   30 d               1   9h          jk

    2f                       3
   = 2                    = 6 4
    5d                     h k
Algebra Cruncher Problems
 Follow this link to try a couple on your own at Cool Math.
 Notice when you select the “Give me a Problem” button
 to try new problems, 2 rows are generated. Look
 carefully between them. That red line indicates this
 problem is a fraction.

 Do your work in a notebook before entering your answer.

 When you select “What’s the Answer?” compare your
 answer with the given answer.

 Keep selecting new problems until you get 3
 consecutive problems correct.
Divide a Polynomial by a Monomial
 Visit this Cool math website to learn about dividing
 a Polynomial by a monomial.

 Be sure to click the “next page” to review the 2
 pages of notes.

 Complete the “Try it” problem on page 2 in your
 notebook.
Try It - Page 2
    ( 4wy − 20w + 6wy − 7 ) ÷ 4wy
         2      2                   2
Try It - Page 2
    ( 4wy − 20w + 6wy − 7 ) ÷ 4wy
              2       2               2


          2       2
      4wy     20w     6wy      7
    =     2
            −     2
                    +     2
                            −     2
      4wy     4wy     4wy     4wy
Try It - Page 2
    ( 4wy − 20w + 6wy − 7 ) ÷ 4wy
              2           2                             2


          2           2
      4wy     20w     6wy      7
    =     2
            −     2
                    +     2
                            −     2
      4wy     4wy     4wy     4wy

            2     5           2 −1       3
      4wy     20 w                         6w         7
    =       −      2
                                     +        2 −1
                                                   −     2
      4wy 2
              1 4y                     2 4 wy        4wy
Try It - Page 2
    ( 4wy − 20w + 6wy − 7 ) ÷ 4wy
              2           2                             2


          2           2
      4wy     20w     6wy      7
    =     2
            −     2
                    +     2
                            −     2
      4wy     4wy     4wy     4wy

            2     5           2 −1       3
      4wy     20 w                         6w         7
    =       −      2
                                     +        2 −1
                                                   −     2
      4wy 2
              1 4y                     2 4 wy        4wy

        5w 3     7
    = 1− 2 +   −    2
         y   2y 4wy
Still a little confused?
 Here’s another tiny lesson dividing a
 polynomial by a monomial.

 Only view the “Steps for Dividing a
 Polynomial by a Monomial.”
It’s Practice time...
 Go to the Regents Prep website to
 practice dividing a polynomial by a
 monomial. Only practice questions 1
 through 7!
 Message or Pronto me if you have
 questions.
Shall we Play a GAME?
 Check your knowledge on Dividing Polynomials by playing
 Jeopardy. Ok, technically it’s called Challenge Board but
 it’s the same idea! There are 4 categories: horseshoes,
 handgrenades, doesn’t count, and polynomial long division.
 Polynomial long division is not covered in Algebra 1 so
 either stay away from this topic or challenge yourself!

 You have the option to play alone or against a friend or
 family member.

 You could even arrange a time with a classmate to meet
 on Pronto to play. Try the App Share feature to see the
 same game board!
Congratulations!
 You’ve finished the notes and practice
 for Dividing a Polynomial by a Monomial.
 You are now ready to proceed to the
 Mastery Assignment.
 Good luck!

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Topic 4 dividing a polynomial by a monomial

  • 1. Dividing polynomials by a monomial Module 10 - Topic 4
  • 2. Dividing a Monomial by a Monomial
  • 3. Dividing a Monomial by a Monomial Apply the rules for dividing exponents:
  • 4. Dividing a Monomial by a Monomial Apply the rules for dividing exponents: Like bases, subtract smaller from the larger exponent to get the new exponent and keep the same base.
  • 5. Dividing a Monomial by a Monomial Apply the rules for dividing exponents: Like bases, subtract smaller from the larger exponent to get the new exponent and keep the same base. If the larger exponent is in the numerator, the result goes in the numerator.
  • 6. Dividing a Monomial by a Monomial Apply the rules for dividing exponents: x5 Like bases, subtract smaller from 3 the larger exponent to get the x new exponent and keep the same base. If the larger exponent is in the numerator, the result goes in the numerator.
  • 7. Dividing a Monomial by a Monomial Apply the rules for dividing exponents: x 5 Like bases, subtract smaller from 3 the larger exponent to get the x new exponent and keep the same base. =x 5− 3 If the larger exponent is in the numerator, the result goes in the numerator.
  • 8. Dividing a Monomial by a Monomial Apply the rules for dividing exponents: x 5 Like bases, subtract smaller from 3 the larger exponent to get the x new exponent and keep the same base. =x 5− 3 If the larger exponent is in the numerator, the result goes in the 2 numerator. =x
  • 9. Dividing a Monomial by a Monomial Apply the rules for dividing exponents: x 5 Like bases, subtract smaller from 3 the larger exponent to get the x new exponent and keep the same base. =x 5− 3 If the larger exponent is in the numerator, the result goes in the 2 numerator. =x If the larger exponent is in the denominator, the result goes in the denominator.
  • 10. Dividing a Monomial by a Monomial Apply the rules for dividing exponents: x 5 a4 Like bases, subtract smaller from 3 9 the larger exponent to get the x a new exponent and keep the same base. =x 5− 3 If the larger exponent is in the numerator, the result goes in the 2 numerator. =x If the larger exponent is in the denominator, the result goes in the denominator.
  • 11. Dividing a Monomial by a Monomial Apply the rules for dividing exponents: x 5 a 4 Like bases, subtract smaller from 3 9 the larger exponent to get the x a new exponent and keep the same base. =x 5− 3 1 = 9− 4 If the larger exponent is in the a numerator, the result goes in the 2 numerator. =x If the larger exponent is in the denominator, the result goes in the denominator.
  • 12. Dividing a Monomial by a Monomial Apply the rules for dividing exponents: x 5 a 4 Like bases, subtract smaller from 3 9 the larger exponent to get the x a new exponent and keep the same base. =x 5− 3 1 = 9− 4 If the larger exponent is in the a numerator, the result goes in the 2 numerator. =x 1 If the larger exponent is in the = 5 denominator, the result goes in a the denominator.
  • 13. Simplify. 5 3 8a b 2 7 6a b
  • 14. Simplify. 5 8a b 3 Reduce the 2 7 numerical part by 6a b dividing the 8 and 6 by 2.
  • 15. Simplify. 5 8a b 3 Reduce the 2 7 numerical part by 6a b dividing the 8 and 4 8a b 5 3 6 by 2. 2 7 3 6a b
  • 16. Simplify. 5 8a b 3 Reduce the 2 7 numerical part by 6a b dividing the 8 and 4 8a b 5 3 6 by 2. 2 7 3 6a b Apply the rules for dividing powers with like bases.
  • 17. Simplify. 5 8a b 3 Reduce the 2 7 numerical part by 6a b dividing the 8 and 4 8a b 5 3 6 by 2. 2 7 3 6a b Apply the rules for 4a 5−2 dividing powers 7− 3 with like bases. 3b 3 And you are done 4a 4 dividing a monomial 3b by a monomial.
  • 18. Simplify each of the following. 8 2 3 5 12d f 27h jk 10 9 9 30d f 9h jk
  • 19. Simplify each of the following. 8 2 3 5 12d f 27h jk 10 9 9 30d f 9h jk 2 2 −1 12 f = 10 − 8 5 30 d
  • 20. Simplify each of the following. 8 2 3 5 12d f 27h jk 10 9 9 30d f 9h jk 2 2 −1 12 f = 10 − 8 5 30 d 2f = 2 5d
  • 21. Simplify each of the following. 8 2 3 5 12d f 27h jk 10 9 9 30d f 9h jk 2 3 12 f 2 −1 27 j = 10 − 8 = 9− 3 9−5 5 30 d 1 9h jk 2f = 2 5d
  • 22. Simplify each of the following. 8 2 3 5 12d f 27h jk 10 9 9 30d f 9h jk 2 3 12 f 2 −1 27 j = 10 − 8 = 9− 3 9−5 5 30 d 1 9h jk 2f 3 = 2 = 6 4 5d h k
  • 23. Algebra Cruncher Problems Follow this link to try a couple on your own at Cool Math. Notice when you select the “Give me a Problem” button to try new problems, 2 rows are generated. Look carefully between them. That red line indicates this problem is a fraction. Do your work in a notebook before entering your answer. When you select “What’s the Answer?” compare your answer with the given answer. Keep selecting new problems until you get 3 consecutive problems correct.
  • 24. Divide a Polynomial by a Monomial Visit this Cool math website to learn about dividing a Polynomial by a monomial. Be sure to click the “next page” to review the 2 pages of notes. Complete the “Try it” problem on page 2 in your notebook.
  • 25. Try It - Page 2 ( 4wy − 20w + 6wy − 7 ) ÷ 4wy 2 2 2
  • 26. Try It - Page 2 ( 4wy − 20w + 6wy − 7 ) ÷ 4wy 2 2 2 2 2 4wy 20w 6wy 7 = 2 − 2 + 2 − 2 4wy 4wy 4wy 4wy
  • 27. Try It - Page 2 ( 4wy − 20w + 6wy − 7 ) ÷ 4wy 2 2 2 2 2 4wy 20w 6wy 7 = 2 − 2 + 2 − 2 4wy 4wy 4wy 4wy 2 5 2 −1 3 4wy 20 w 6w 7 = − 2 + 2 −1 − 2 4wy 2 1 4y 2 4 wy 4wy
  • 28. Try It - Page 2 ( 4wy − 20w + 6wy − 7 ) ÷ 4wy 2 2 2 2 2 4wy 20w 6wy 7 = 2 − 2 + 2 − 2 4wy 4wy 4wy 4wy 2 5 2 −1 3 4wy 20 w 6w 7 = − 2 + 2 −1 − 2 4wy 2 1 4y 2 4 wy 4wy 5w 3 7 = 1− 2 + − 2 y 2y 4wy
  • 29. Still a little confused? Here’s another tiny lesson dividing a polynomial by a monomial. Only view the “Steps for Dividing a Polynomial by a Monomial.”
  • 30. It’s Practice time... Go to the Regents Prep website to practice dividing a polynomial by a monomial. Only practice questions 1 through 7! Message or Pronto me if you have questions.
  • 31. Shall we Play a GAME? Check your knowledge on Dividing Polynomials by playing Jeopardy. Ok, technically it’s called Challenge Board but it’s the same idea! There are 4 categories: horseshoes, handgrenades, doesn’t count, and polynomial long division. Polynomial long division is not covered in Algebra 1 so either stay away from this topic or challenge yourself! You have the option to play alone or against a friend or family member. You could even arrange a time with a classmate to meet on Pronto to play. Try the App Share feature to see the same game board!
  • 32. Congratulations! You’ve finished the notes and practice for Dividing a Polynomial by a Monomial. You are now ready to proceed to the Mastery Assignment. Good luck!

Editor's Notes