Appendix A.3 Polynomials and Factoring A33 A.3 Exercises See CalcChat.com for tutorial help and worked-out solutions to odd-numbered exercises. Vocabulary: Fill in the blanks. 1. For the polynomial a, x" + an_x"-1 + . . . + ax + do, an # 0, the degree is the leading coefficient is . , and the constant term is 2. A polynomial with one term is a while a polynomial with two terms is a and a polynomial with three terms is a d solast 80-50 3. To add or subtract polynomials, add or subtract the their coefficients. by adding or subtracting 4. The letters in "FOIL" stand for F 0 and L 5. The process of writing a polynomial as a product is called 6. A polynomial is when each of its factors is prime. 7. A. is the square of a binomial, and it has the form u2 + 2uv + v2 or u2 - 2uv + v2. 8. Sometimes, polynomials with more than three terms can be factored by Skills and Applications 95 - 94 Writing Polynomials in Standard Form 33. [(x - 3) + y ]2 34. [(x + 1) - y] In Exercises 9-14, (a) write the polynomial in 35. [(m - 3) + n][(m - 3) - n] standard form, (b) identify the degree and leading coefficient of the polynomial, and 36. [(x - 3y) + z][(x - 3y) - z] (c) state whether the polynomial is a 0810 Factoring Out a Common Factor In monomial, a binomial, or a trinomial. Exercises 37-40, factor out the common 9. 7x 10. 3 factor. 11. 14x - 5x5 12. 3 + 2x 37. 2x3 - 6x 38. 323 - 672 + 9z 13. 1 + 6x4 - 4 14. -y + 25y2 + 1 39. 3x(x - 5) + 8(x - 5) 40. (x+ 3)2- 4(x + 3) 0130 Adding or Subtracting Polynomials In Factoring the Difference of Two Exercises 15-18, add or subtract and write Squares In Exercises 41-44, completely the result in standard form. factor the difference of two squares. 15. (6x + 5) - (8x + 15) 41. 25y2 - 4 42. 81 - 3672 16. (2x2 + 1) - (x2 - 2x + 1) 43. (x - 1)2 - 4 44. 25 - (2 + 5)2 17. (15x2 - 6) + (-8.3x3 - 14.7x2 -17) 0:30 Factoring a Perfect Square Trinomial 18. (15.6w4 - 14w - 17.4) + (16.9w4 - 9.2w + 13) In Exercises 45-50, factor the perfect square Multiplying Polynomials In Exercises trinomial. 19-36, multiply the polynomials. 45. x2 - 4x + 4 46. 412 + 4t + 1 19. 3x(x2 - 2x + 1) 20. y2 (4y2 + 2y - 3) 47. 25z2 - 30z + 9 21. -5z(3z - 1) 22. - 3x(5x + 2) 48. 36y2 + 84y + 49 23. (3x - 5)(2x + 1) 24. (7x - 2)(4x - 3) 49. 4y2 - 12y + 9 25. (x2 - x+ 2) (x2 + x + 1) 50. 9u2 + 24uv + 16v2 26. (2x2 - x + 4)(x2 + 3x + 2) OWiO Factoring the Sum or Difference of 27. (x + 10)(x - 10) Two Cubes In Exercises 51-54, factor the 28. ( 4a + 56) (4a - 56) sum or difference of two cubes. 29. (2x + 3) 2 30. (8x + 3) 2 51. x3 + 125 52. x3 - 8 31. (x + 3) 3 32. (3x + 2y) 3 53. 813 - 1 54. 27+3 + 8