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- 1. Dividing polynomials by a monomial
- 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 Homework Assignment. Good luck!

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