Chap6 Section2

Elementary and Intermediate Algebra: Graphs & Models (3rd Edition)

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Unformatted text preview: Section 6.2 Zeros of Polynomials 577 Version: Fall 2007 6.2 Exercises In Exercises 1- 6 , use direct substitu- tion to show that the given value is a zero of the given polynomial. 1. p ( x ) = x 3 − 3 x 2 − 13 x + 15, x = − 3 2. p ( x ) = x 3 − 2 x 2 − 13 x − 10, x = − 2 3. p ( x ) = x 4 − x 3 − 12 x 2 , x = 4 4. p ( x ) = x 4 − 2 x 3 − 3 x 2 , x = − 1 5. p ( x ) = x 4 + x 2 − 20, x = − 2 6. p ( x ) = x 4 + x 3 − 19 x 2 + 11 x + 30, x = − 1 In Exercises 7- 28 , identify all of the zeros of the given polynomial without the aid of a calculator. Use an alge- braic technique and show all work (fac- tor when necessary) needed to obtain the zeros. 7. p ( x ) = ( x − 2)( x + 4)( x − 5) 8. p ( x ) = ( x − 1)( x − 3)( x + 8) 9. p ( x ) = − 2( x − 3)( x + 4)( x − 2) 10. p ( x ) = − 3( x + 1)( x − 1)( x − 8) 11. p ( x ) = x ( x − 3)(2 x + 1) 12. p ( x ) = − 3 x ( x + 5)(3 x − 2) 13. p ( x ) = − 2( x + 3)(3 x − 5)(2 x + 1) 14. p ( x ) = 3( x − 2)(2 x + 5)(3 x − 4) 15. p ( x ) = 3 x 3 + 5 x 2 − 12 x − 20 Copyrighted material. See: http://msenux.redwoods.edu/IntAlgText/ 1 16. p ( x ) = 3 x 3 + x 2 − 12 x − 4 17. p ( x ) = 2 x 3 + 5 x 2 − 2 x − 5 18. p ( x ) = 2 x 3 − 5 x 2 − 18 x + 45 19. p ( x ) = x 4 + 4 x 3 − 9 x 2 − 36 x 20. p ( x ) = − x 4 + 4 x 3 + x 2 − 4 x 21. p ( x ) = − 2 x 4 − 10 x 3 + 8 x 2 + 40 x 22. p ( x ) = 3 x 4 + 6 x 3 − 75 x 2 − 150 x 23. p ( x ) = 2 x 3 − 7 x 2 − 15 x 24. p ( x ) = 2 x 3 − x 2 − 10 x 25. p ( x ) = − 6 x 3 + 4 x 2 + 16 x 26. p ( x ) = 9 x 3 + 3 x 2 − 30 x 27. p ( x ) = − 2 x 7 − 10 x 6 + 8 x 5 + 40 x 4 28. p ( x ) = 6 x 5 − 21 x 4 − 45 x 3 578 Chapter 6 Polynomial Functions Version: Fall 2007 In Exercises 29- 34 , the graph of a poly- nomial is given. Perform each of the fol- lowing tasks. i. Copy the image onto your homework paper. Label and scale your axes, then label each x-intercept with its coordinates. ii. Identify the zeros of the polynomial. 29. x 10 y 10 30. x 10 y 10 31. x 10 y 10 32. x 10 y 10 33. x 10 y 10 34. x 10 y 10 Section 6.2 Zeros of Polynomials 579 Version: Fall 2007 For each of the polynomials in Exercises 35- 46 , perform each of the following tasks. i. Factor the polynomial to obtain the zeros. Show your work. ii. Set up a coordinate system on graph paper. Label and scale the horizontal axis. Use the zeros and end-behavior to help sketch the graph of the poly- nomial without the use of a calcula- tor. iii. Verify your result with a graphing cal- culator. 35. p ( x ) = 5 x 3 + x 2 − 45 x − 9 36. p ( x ) = 4 x 3 + 3 x 2 − 64 x − 48 37. p ( x ) = 4 x 3 − 12 x 2 − 9 x + 27 38. p ( x ) = x 3 + x 2 − 16 x − 16 39. p ( x ) = x 4 + 2 x 3 − 25 x 2 − 50 x 40. p ( x ) = − x 4 − 5 x 3 + 4 x 2 + 20 x 41. p ( x ) = − 3 x 4 − 9 x 3 + 3 x 2 + 9 x 42. p ( x ) = 4 x 4 − 29 x 2 + 25 43. p ( x ) = − x 3 − x 2 + 20 x 44. p ( x ) = 2 x 3 − 7 x 2 − 30 x 45. p ( x ) = 2 x 3...
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Chap6 Section2 - Section 6.2 Zeros of Polynomials 577...

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