Algebra II Po lynomials: Operations and Functions

1. Algebra II Polynomials: Operations and Functions IMPORTANT TIP: Throughout this unit, it is 
extremely important that you, as a teacher, 
emphasize correct vocabulary and make sure 
students truly know the difference between 
monomials and polynomials. Having a solid 
understanding of rules that accompany each will 
give them a strong foundation for future math 
classes. Teacher 2013-09-25 www.njctl.org

2. Table of Contents click on the topic to go to that section Properties of Exponents Review Adding and Subtracting Polynomials Multiplying a Polynomial by a Monomial Multiplying Polynomials Special Binomial Products Dividing a Polynomial by a Monomial Dividing a Polynomial by a Polynomial Characteristics of Polynomial Functions Analyzing Graphs and Tables of Polynomial Functions Zeros and Roots of a Polynomial Function Writing Polynomials from its Zeros

3. Properties of Exponents Review Return to Table of Contents

4. Exponents Goals and Objectives Students will be able to simplify complex expressions containing exponents.

5. Exponents Why do we need this? Exponents allow us to condense bigger expressions into smaller ones. Combining all properties of powers together, we can easily take a complicated expression and make it simpler.

6. Properties of Exponents

7. Exponents Multiplying powers of the same base: (x4y3)(x3y) Have students think about what the expression means and then use the rule as a short cut. For example: (x4y3)(x3y) = x x x x y y y x x x y = x7y4 The rules are a quick way to get an answer. Teacher Can you write this expression in another way?? . . . . . . . . . .

8. Exponents (-3a3b2)(2a4b3) -6a7b5 (-4p2q4n)(3p3q3n) -12p5q7n2 Simplify: Teacher (-3a3b2)(2a4b3) (-4p2q4n)(3p3q3n)

9. Exponents Work out: . xy3 x5y4 (3x2y3)(2x3y) 6x5y4 Teacher x6y7 . (3x2y3)(2x3y) xy3 x5y4

10. Exponents (m4np)(mn3p2) 1 Simplify: B Teacher A m4n3p2 B m5n4p3 C mnp9 D Solution not shown

11. Exponents D (-3x3y)(4xy4) -12x4y5 2 Simplify: (-3x3y)(4xy4) Teacher A x4y5 B 7x3y5 C -12x3y4 D Solution not shown

12. Exponents . 3 Work out: 2p2q3 4p2q4 D 2p2q3 4p2q4 8p4q7 Teacher . A 6p2q4 B 6p4q7 C 8p4q12 D Solution not shown

13. 5m2q3 10m4q5 Exponents . 4 Simplify: A Teacher A 50m6q8 B 15m6q8 C 50m8q15 D Solution not shown

14. Exponents 5 Simplify: (-6a4b5)(6ab6) B Teacher A a4b11 B -36a5b11 C -36a4b30 D Solution not shown

15. Exponents Dividing numbers with the same base: Have students think about what the expression means and then use the rule as a short cut. For example: x4y3 = x x x x y y y = xy2 The rules are a quick way to get an answer. Teacher . . . . . . . . . x3y x x x y = 4m

16. Exponents Teacher Simplify:

17. Exponents Try... Teacher

18. Exponents A 6 Divide: Teacher C A D Solutions not shown B

19. Exponents 7 Simplify: D Teacher C A D Solution not shown B

20. Exponents A 8 Work out: Teacher C A D Solution not shown B

21. Exponents 9 Divide: C Teacher C A D Solution not shown B

22. Exponents D 10 Simplify: Teacher C A D Solution not shown B

23. Exponents Power to a power: Have students think about what the expression means and then use the rule as a short cut. For example: The rules are a quick way to get an answer. Teacher .

24. Exponents Simplify: Teacher

25. Exponents Try: Teacher

26. Exponents D 11 Work out: Teacher C A B D Solution not shown

27. Exponents 12 Work out: B Teacher C A D Solution not shown B

28. Exponents C 13 Simplify: Teacher C A D Solution not shown B

29. Exponents D 14 Simplify: Teacher C A D Solution not shown B

30. Exponents 15 Simplify: C Teacher C A D Solution not shown B

31. Exponents Negative and zero exponents: Teacher Spend time showing students how negatives and zeros occur. Why is this? Work out the following:

32. Exponents Sometimes it is more appropriate to leave answers with positive exponents, and other times, it is better to leave answers without fractions. You need to be able to translate expressions into either form. Teacher Write with positive exponents: Write without a fraction:

33. Exponents Simplify and write the answer in both forms. Teacher

34. Exponents Simplify and write the answer in both forms. Teacher

35. Exponents Teacher Simplify:

36. Exponents Write the answer with positive exponents. Teacher

37. Exponents B 16 Simplify and leave the answer with positive exponents: Teacher A C B D Solution not shown

38. Exponents A 17 Simplify. The answer may be in either form. Teacher A C B D Solution not shown

39. Exponents 18 Write with positive exponents: D Teacher A C B D Solution not shown

40. Exponents 19 Simplify and write with positive exponents: D Teacher A C B D Solution not shown

41. Exponents 20 Simplify. Write the answer with positive exponents. C Teacher A C B D Solution not shown

42. Exponents 21 Simplify. Write the answer without a fraction. A Teacher A C B D Solution not shown

43. Exponents Combinations Teacher Usually, there are multiple rules needed to simplify problems with exponents. Try this one. Leave your answers with positive exponents. **Much of the time it is a good idea to simplify inside the parentheses first.

44. Exponents When fractions are to a negative power, a short cut is to flip the fraction and make the exponent positive. Teacher Try...

45. Exponents Two more examples. Leave your answers with positive exponents. Teacher

46. Exponents 22 Simplify and write with positive exponents: D Teacher A C B D Solution not shown

47. Exponents 23 Simplify. Answer can be in either form. B Teacher A C B D Solution not shown

48. Exponents 24 Simplify and write with positive exponents: B Teacher A C B D Solution not shown

49. Exponents 25 Simplify and write without a fraction: A Teacher A C B D Solution not shown

50. Exponents 26 Simplify. Answer may be in any form. D Teacher A C B D Solution not shown