Chapter 6: Exercises with Answers (all sections combined)

Section 6.2 Zeros of Polynomials 5776.2 ExercisesIn Exercises 1-6, use direct substitutionto show that the given value is azero of the given polynomial.1. p(x) = x 3 − 3x 2 − 13x + 15, x = −32. p(x) = x 3 − 2x 2 − 13x − 10, x = −23. p(x) = x 4 − x 3 − 12x 2 , x = 44. p(x) = x 4 − 2x 3 − 3x 2 , x = −15. p(x) = x 4 + x 2 − 20, x = −26. p(x) = x 4 + x 3 − 19x 2 + 11x + 30,x = −1In Exercises 7-28, identify all of thezeros of the given polynomial withoutthe aid of a calculator. Use an algebraictechnique and show all work (factorwhen necessary) needed to obtain thezeros.7. p(x) = (x − 2)(x + 4)(x − 5)16. p(x) = 3x 3 + x 2 − 12x − 417. p(x) = 2x 3 + 5x 2 − 2x − 518. p(x) = 2x 3 − 5x 2 − 18x + 4519. p(x) = x 4 + 4x 3 − 9x 2 − 36x20. p(x) = −x 4 + 4x 3 + x 2 − 4x21. p(x) = −2x 4 − 10x 3 + 8x 2 + 40x22. p(x) = 3x 4 + 6x 3 − 75x 2 − 150x23. p(x) = 2x 3 − 7x 2 − 15x24. p(x) = 2x 3 − x 2 − 10x25. p(x) = −6x 3 + 4x 2 + 16x26. p(x) = 9x 3 + 3x 2 − 30x27. p(x) = −2x 7 − 10x 6 + 8x 5 + 40x 428. p(x) = 6x 5 − 21x 4 − 45x 38. 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)(2x + 1)12. p(x) = −3x(x + 5)(3x − 2)13. p(x) = −2(x + 3)(3x − 5)(2x + 1)14. p(x) = 3(x − 2)(2x + 5)(3x − 4)15. p(x) = 3x 3 + 5x 2 − 12x − 201Copyrighted material. See: http://msenux.redwoods.edu/IntAlgText/Version: Fall 2007