# polynomial vs. non-polynomial functions even vs. odd ... ?· 21. describe the degree and leading...

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• CC Algebra II HW #22

Polynomial vs. Non-Polynomial Functions Even vs. Odd Functions; End Behavior

Read 4.1 Examples 1-3 Section 4.1 2. Which One Doesn't Belong? Which function does not belong with the other three? Explain your reasoning.

In Exercises 3–8, decide whether the function is a polynomial function. If so, write it in standard form and state its degree, type, and leading coefficient. (See Example 1.) 3. 2653)( 23 +−+−= xxxxf 5. xxxxxf 2689)( 234 +−+= − 7. xxxxxh +−+−= 2

1342 3 5 87)(

9. Describe and correct the error in analyzing the function 113978)( 243 +−−−= xxxxxf .

11. Evaluate the function for the given value of x. (See Example 2.) 2 ;61223)( 34 −=−−+−= xxxxxh

In Exercises 17-20, describe the end behavior of the graph of the function. (See Example 3.) 17. 29675)( 234 ++−+−= xxxxxh 19. 284 1517122)( xxxxf +++−=

Name ____________________________ Period ___ Row___ Date ___________

• 21. Describe the degree and leading coefficient of the polynomial function using the graph.

23. Using Structure Determine whether the function is a polynomial function. If so, write it in standard form and state its degree, type, and leading coefficient.

414295)( 552432 53 −−−++−+= − xxxxxxxxxf

Section 4.8 Determine whether the function is even, odd, or neither. (See Example 4.)

41. 23)( 24 −+= xxxf 43. 15)( 2 ++= xxxg 44. 92)( 3 −+−= xxxf

• CC Algebra II HW #23

Section 4.1 Analyzing Relationships In Exercises 33–36, describe the x-values for which (a) f is increasing or decreasing, (b) 0)( >xf , and (c) 0)(

• In Exercises 17–24, find the product. (See Example 3.) 17. )135(7 23 ++ xxx 19. )32)(645( 2 +−+− xxx 23. )12)(793( 23 +−+− xxxx 25. Error Analysis: Describe and correct the error in performing the operation.

In Exercises 27–32, find the product of the binomials. (See Example 4.) 27. )4)(2)(3( ++− xxx

• CC Algebra II Name _________________________ HW #24 Period ___ Row ____ Date ______

Factoring with GCF, Difference of Two Squares, By Grouping, & Trinomials (a=1) Read 4.4 / Examples 1 & 3

Section 4.4 In Exercises 5–12, factor the polynomial completely. (See Example 1.) 5. xxx 242 23 −− 7. 35 1923 pp −

6. 35 1004 kk − 8. 456 64242 mmm +−

21. Error Analysis Describe and correct the error in factoring the polynomial. In Exercises 23–30, factor the polynomial completely. (See Example 3.) 23. 3065 23 −+− yyy 27. 3248 23 +−− xxx

25. 488183 23 +++ aaa 29. 369164 23 +−− qqq

• CC Algebra II Name _________________________ HW #25 Period ___ Row ____ Date ______

Factoring with Sum/Difference of Cubes, Quadratic Form, & Trinomials (a > 1) Read 4.4 / Examples 2 & 4

Section 4.4 In Exercises 5–12, factor the polynomial completely. (See Example 1.) 9. 234 1892 qqq −+

11. 8910 61910 www +−

In Exercises 13–20, factor the polynomial completely. (See Example 2.) 13. 643 +x 17. 69 1923 hh −

15. 3433 −g 19. 47 25016 tt +

In Exercises 31–38, factor the polynomial completely. (See Example 4.) 31. 49k4 − 9 35. 16z4 − 81 33. c4 + 9c2 + 20 37. 3r8 + 3r5 − 60r2

• CC Algebra II HW #26

Dividing Polynomials Including Synthetic Division Read 4.3 Examples 1-3

Section 4.3 Divide using polynomial long division. (See Example 1.) 5. )4()17( 2 −÷−+ xxx 7. )1()2( 223 −÷+++ xxxx In Exercises 11–18, divide using synthetic division. (See Examples 2 and 3.) 11. )4()18( 2 −÷++ xxx 13. )5()72( 2 +÷+− xxx 15. )3()9( 2 −÷+ xx 17. )6()121385( 234 −÷−+−− xxxxx

Name ____________________________ Period ___ Row___ Date ___________

• Error Analysis Describe and correct the error in using synthetic division to divide x3 − 5x + 3 by x − 2.

Maintaining Mathematical Proficiency Find the zero(s) of the function. (Sections 3.1 and 3.2) 41. 96)( 2 +−= xxxf 43. 4914)( 2 ++= xxxg

• CC Algebra II HW #27

Remainder Theorem Read 4.3 Example 4

Section 4.3 6. Divide using polynomial long division. (See Example 1.) )5()5143( 2 −÷−− xxx In Exercises 25–32, use synthetic division to evaluate the function for the indicated value of x. (See Example 4.) 25. 1 ;308)( 2 −=+−−= xxxxf 27. 2 ;342)( 23 =++−= xxxxxf 29. 6 ;16)( 3 =+−= xxxxf 31. 3 ;176)( 24 =+−+= xxxxxf 33. Making an Argument You use synthetic division to divide )(xf by (x − a) and find that the remainder equals 15. Your friend concludes that af =)15( . Is your friend correct? Explain your reasoning.

Name ____________________________ Period ___ Row___ Date ___________

• 34. Thought Provoking A polygon has an area represented by A = 4x2 + 8x + 4. The figure has at least one dimension equal to 2x + 2. Draw the figure and label its dimensions.

• CC Algebra II HW #28

The Factor Theorem Read 4.4 Examples 5-7

Section 4.4 In Exercises 39–44, determine whether the binomial is a factor of the polynomial function. (See Example 5.) 39. 4 ;603752)( 23 −−−+= xxxxxf 41. 3 ;9156)( 345 +−−= xxxxxh In Exercises 45–50, show that the binomial is a factor of the polynomial. Then factor the function completely. (See Example 6.) 46. 5 ;4595)( 23 −+−−= xxxxxt 47. 6 ;4886)( 34 −+−−= xxxxxf 49. 7 ;8437)( 3 ++−= xxxxr

Name ____________________________ Period ___ Row___ Date ___________

• Analyzing Relationships In Exercises 51–54, match the function with the correct graph. Explain your reasoning. 51. )1)(3)(2()( +−−= xxxxf 52. )2)(1)(2()( −++= xxxxxg

53. )1)(3)(2()( −++= xxxxh 54. )2)(1)(2()( +−−= xxxxxk

69. Comparing Methods You are taking a test where calculators are not permitted. One question asks you to evaluate g(7) for the function g(x) = x3 − 7x2 − 4x + 28. You use the Factor Theorem and synthetic division and your friend uses direct substitution. Whose method do you prefer? Explain your reasoning. Maintaining Mathematical Proficiency Solve the quadratic equation by factoring. (Section 3.1) 79. 3x2 −11x + 10 = 0 Solve the quadratic equation by completing the square. (Section 3.3) 83. 3x2 + 30x + 63 = 0

• CC Algebra II HW # 29

Sketching Polynomial Functions Using Zeros and End Behavior Read 4.5 Examples 1, 2 and 5; 4.6 Example 1

Section 4.5 In Exercises 3–12, solve the equation. (See Example 1.) 3. 01223 =−− zzz 9. cccc 361262 234 −=− In Exercises 13–20, find the zeros of the function. Then sketch a graph of the function. (See Example 2.) 13. 234 6)( xxxxh −+= 17. 234 6084)( xxxxg ++−= 19. 99)( 23 ++−−= xxxxh

In Exercises 41–46, write a polynomial function f of least degree that has a leading coefficient of 1 and the given zeros. (See Example 5.) 41. –2, 3, 6 45. 53 ,0 ,6 −−

Name ____________________________ Period ___ Row___ Date ___________

• Section 4.6 In Exercises 3–8, identify the number of solutions or zeros. (See Example 1.) 3. 042 234 =+−+ xxxx 7. 224)( 735 −+−= ssssg In Exercises 17–20, determine the number of imaginary zeros for the function with the given degree and graph. Explain your reasoning. 17. Degree: 4

18. Degree: 5

20. Degree: 3

• CC Algebra II HW #30

Analyzing Graphs of Polynomial Functions Read 4.8 Examples 1 and 3

Section 4.8 1. Complete the Sentence A local maximum or local minimum of a polynomial function occurs at a _____________________ point of the graph of the function.

2. Writing Explain what a local maximum of a function is and how it may be different from the maximum value of the function. Analyzing Relationships In Exercises 3–6, match the function with its graph. 3. )2)(2)(1()( +−−= xxxxf 4. )1()2()( 2 ++= xxxh 5. )2)(1)(1()( +−+= xxxxg 6. )2()1()( 2 +−= xxxf

In Exercises 7–14, graph the function. (See Example 1: Be sure to use this method, and not just graph it on your calculator!) 7. )1()2()( 2 +−= xxxf 9. )3)(1()1()( 2 −−+= xxxxh

Error Analysis Describe and correct the error in using factors to graph f. 15. 2)1)(2()( −+= xxxf

Name ____________________________ Period ___ Ro