1 Foundations 2 Solving Linear Equations 3 Graphs And Functions 4 Systems Of Linear Equations 5 Polynomials And Polynomial Functions 6 Factoring 7 Rational Expressions And Functions 8 Roots And Radicals 9 Quadratic Equations And Functions 10 Exponential And Logarithmic Functions 11 Conics 12 Sequences, Series And Binomial Theorem Chapter5: Polynomials And Polynomial Functions
5.1 Add And Subtract Polynomials 5.2 Properties Of Exponents And Scientific Notation 5.3 Multiply Polynomials 5.4 Dividing Polynomials Chapter Questions Section5.1: Add And Subtract Polynomials
Problem 5.1TI: Determine whether each polynomial is a monomial, binomial, trinomial, or other polynomial. Then,... Problem 5.2TI: Determine whether each polynomial is a monomial, binomial, trinomial, or other polynomial. Then,... Problem 5.3TI: Add or subtract: (a) 12q2+9q2 (b) 8mn3(5mn3) . Problem 5.4TI: Add or subtract: (a) 15c2+8c2 (b) 15y2z3(5y2z3) . Problem 5.5TI: Add: (a) 8y2+3z23y2 (b) m2n28m2+4n2 . Problem 5.6TI: Add: (a) 3m2+n27m2 (b) pq26p5q2 . Problem 5.7TI: Find the sum: (7x24x+5)+(x27x+3) . Problem 5.8TI: Find the sum: (14y2+6y4)+(3y2+8y+5) . Problem 5.9TI: Find the difference: (8x2+3x19)(7x214) . Problem 5.10TI: Find the difference: (9b25b4)(3b25b7) . Problem 5.11TI: Subtract (a2+5ab6b2) from (a2+b2) . Problem 5.12TI: Subtract (m27mn3n2) from (m2+n2) . Problem 5.13TI: Find the sum: (3x24xy+5y2)+(2x2xy) . Problem 5.14TI: Find the sum: (2x23xy2y2)+(5x23xy) . Problem 5.15TI: Simplify: (x3x2y)(xy2+y3)+(x2y+xy2) . Problem 5.16TI: Simplify: (p3p2q)+(pq2+q3)(p2q+pq2) . Problem 5.17TI: For the function f(x)=3x2+2x15 , find (a) f(3) (b) f(5) (c) f(0) . Problem 5.18TI: For the function g(x)=5x2x4 , find (a) g(2) (b) g(1) (c) g(0) . Problem 5.19TI: The polynomial function h(t)=16t2+150 gives the height of a stone t seconds after it is dropped from... Problem 5.20TI: The polynomial function h(t)=16t2+175 gives the height of a ball t seconds after it is dropped from... Problem 5.21TI: For functions f(x)=2x24x+3 and g(x)=x22x6 , find (a) (f+g)(x) (b) (f+g)(3) (c) (fg)(x) (d) (fg)(2) . Problem 5.22TI: For functions f(x)=5x24x1 and g(x)=x2+3x+8 , find (a) (f+g)(x) (b) (f+g)(3) (c) (fg)(x) (d) (fg)(2)... Problem 1E: In the following exercises, determine if the polynomial is a monomial, binomial, trinomial, or other... Problem 2E: In the following exercises, determine if the polynomial is a monomial, binomial, trinomial, or other... Problem 3E: In the following exercises, determine if the polynomial is a monomial, binomial, trinomial, or other... Problem 4E: In the following exercises, determine if the polynomial is a monomial, binomial, trinomial, or other... Problem 5E: In the following exercises, determine if the polynomial is a monomial, binomial, trinomial, or other... Problem 6E: In the following exercises, determine if the polynomial is a monomial, binomial, trinomial, or other... Problem 7E: In the following exercises, determine if the polynomial is a monomial, binomial, trinomial, or other... Problem 8E: In the following exercises, determine if the polynomial is a monomial, binomial, trinomial, or other... Problem 9E: In the following exercises, add or subtract the monomials. 9. (a) 7x2+5x2 (b) 4a9a Problem 10E: In the following exercises, add or subtract the monomials. 10. (a) 4y3+6y3 (b) y5y Problem 11E: In the following exercises, add or subtract the monomials. 11. (a) 12w+18w (b) 7x2y(12x2y) Problem 12E: In the following exercises, add or subtract the monomials. 12. (a) 3m+9m (b) 51yz2(8yz2) Problem 13E: In the following exercises, add or subtract the monomials. 13. 7x2+5x2+4a9a Problem 14E: In the following exercises, add or subtract the monomials. 14. 4y3+6y3y5y Problem 15E: In the following exercises, add or subtract the monomials. 15. 12w+18w+7x2y(12x2y) Problem 16E: In the following exercises, add or subtract the monomials. 16. 3m+9m+15yz2(8yz2) Problem 17E: In the following exercises, add or subtract the monomials. 17. (a) 5b17b (b) 3xy(8xy)+5xy Problem 18E: In the following exercises, add or subtract the monomials. 18. (a) 10x35x (b) 17mn2(9mn2)+3mn2 Problem 19E: In the following exercises, add or subtract the monomials. 19. (a) 12a+5b22a (b) pq24p3q2 Problem 20E: In the following exercises, add or subtract the monomials. 20. (a) 14x3y13x (b) a2b4a5ab2 Problem 21E: In the following exercises, add or subtract the monomials. 21. (a) 2a2+b26a2 (b) x2y3x+7xy2 Problem 22E: In the following exercises, add or subtract the monomials. 22. (a) 5u2+4v26u2 (b) 12a+8b Problem 23E: In the following exercises, add or subtract the monomials. 23. (a) xy25x5y2 (b) 19y+5z Problem 24E: In the following exercises, add or subtract the monomials. 24. 12a+5b22a+pq24p3q2 Problem 25E: In the following exercises, add or subtract the monomials. 25. 14x3y13x+a2b4a5ab2 Problem 26E: In the following exercises, add or subtract the monomials. 26. 2a2+b26a2+x2y3x+7xy2 Problem 27E: In the following exercises, add or subtract the monomials. 27. 5u2+4v26u2+12a+8b Problem 28E: In the following exercises, add or subtract the monomials. 28. xy25x5y2+19y+5z Problem 29E: In the following exercises, add or subtract the monomials. 29. Add: 4a,3b,8a Problem 30E: In the following exercises, add or subtract the monomials. 30. Add: 4x,3y,3x Problem 31E: In the following exercises, add or subtract the monomials. 31. Subtract 5x6 from 12x6 Problem 32E: In the following exercises, add or subtract the monomials. 32. Subtract 2p4 from 7p4 Problem 33E: In the following exercises, add the polynomials. 33. (5y2+12y+4)+(6y28y+7) Problem 34E: In the following exercises, add the polynomials. 34. (4y2+10y+3)+(8y26y+5) Problem 35E: In the following exercises, add the polynomials. 35. (x2+6x+8)+(4x2+11x9) Problem 36E: In the following exercises, add the polynomials. 36. (y2+9y+4)+(2y25y1) Problem 37E: In the following exercises, add the polynomials. 37. (8x25x+2)+(3x2+3) Problem 38E: In the following exercises, add the polynomials. 38. (7x29x+2)+(6x24) Problem 39E: In the following exercises, add the polynomials. 39. (5a2+8)+(a24a9) Problem 40E: In the following exercises, add the polynomials. 40. (p26p18)+(2p2+11) Problem 41E: In the following exercises, subtract the polynomials. 41. (4m26m3)(2m2+m7) Problem 42E: In the following exercises, subtract the polynomials. 42. (3b24b+1)(5b2b2) Problem 43E: In the following exercises, subtract the polynomials. 43. (a2+8a+5)(a23a+2) Problem 44E: In the following exercises, subtract the polynomials. 44. (b27b+5)(b22b+9) Problem 45E: In the following exercises, subtract the polynomials. 45. (12s215s)(s9) Problem 46E: In the following exercises, subtract the polynomials. 46. (10r220r)(r8) Problem 47E: In the following exercises, subtract the polynomials. 47. Subtract (9x2+2) from (12x2x+6) Problem 48E: In the following exercises, subtract the polynomials. 48. Subtract (5y2y+12) from (10y28y20) Problem 49E: In the following exercises, subtract the polynomials. 49. Subtract (7w24w+2) from (8w2w+6) Problem 50E: In the following exercises, subtract the polynomials. 50. Subtract (5x2x+12) from (9x26x20) Problem 51E: In the following exercises, find the difference of the polynomials. 51. Find the difference of... Problem 52E: In the following exercises, find the difference of the polynomials. 52. Find the difference of... Problem 53E: In the following exercises, add the polynomials. 53. (7x22xy+6y2)+(3x25xy) Problem 54E: In the following exercises, add the polynomials. 54. (5x24xy3y2)+(2x27xy) Problem 55E: In the following exercises, add the polynomials. 55. (7m2+mn8n2)+(3m2+2mn) Problem 56E: In the following exercises, add the polynomials. 56. (2r23rs2s2)+(5r23rs) Problem 57E: In the following exercises, add or subtract the polynomials. 57. (a2b2)(a2+3ab4b2) Problem 58E: In the following exercises, add or subtract the polynomials. 58. (m2+2n2)(m28mnn2) Problem 59E: In the following exercises, add or subtract the polynomials. 59. (p33p2q)+(2pq2+4q3)(3p2q+pq2) Problem 60E: In the following exercises, add or subtract the polynomials. 60. (a32a2b)+(ab2+b3)(3a2b+4ab2) Problem 61E: In the following exercises, add or subtract the polynomials. 61. (x3x2y)(4xy2y3)+(3x2yxy2) Problem 62E: In the following exercises, add or subtract the polynomials. 62. (x32x2y)(xy23y3)(x2y4xy2) Problem 63E: In the following exercises, find the function values for each polynomial function. 63. For the... Problem 64E: In the following exercises, find the function values for each polynomial function. 64. For the... Problem 65E: In the following exercises, find the function values for each polynomial function. 65. For the... Problem 66E: In the following exercises, find the function values for each polynomial function. 66. For the... Problem 67E: In the following exercises, find the height for each polynomial function. 67. A painter drops a... Problem 68E: In the following exercises, find the height for each polynomial function. 68. A girl drops a ball... Problem 69E: In the following exercises, find the height for each polynomial function. 69. A manufacturer of... Problem 70E: In the following exercises, find the height for each polynomial function. 70. A manufacturer of the... Problem 71E: In the following exercises, find the height for each polynomial function. 71. The polynomial... Problem 72E: In the following exercises, find the height for each polynomial function. 72. The polynomial... Problem 73E: In each example, find (a) (f+g)(x)(b) (f+g)(2)(c) (fg)(x)(d) (fg)(3). 73. f(x)=2x24x+1 and... Problem 74E: In each example, find (a) (f+g)(x)(b) (f+g)(2)(c) (fg)(x)(d) (fg)(3). 74. f(x)=4x27x+3 and... Problem 75E: In each example, find (a) (f+g)(x)(b) (f+g)(2)(c) (fg)(x)(d) (fg)(3). 75. f(x)=3x3x22x+3 and... Problem 76E: In each example, find (a) (f+g)(x)(b) (f+g)(2)(c) (fg)(x)(d) (fg)(3). 76. f(x)=5x3x2+3x+4 and... Problem 77E: Using your own words, explain the difference between a monomial, a binomial, and a trinomial. Problem 78E: Using your own words, explain the difference between a polynomial with five terms and a polynomial... Problem 79E: Ariana thinks the sum 6y2+5y4 is 11y6. What is wrong with her reasoning? Problem 80E: Is every trinomial a second degree polynomial? If not, give an example. Problem 5.6TI: Add: (a) 3m2+n27m2 (b) pq26p5q2 .
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Use the integral test to see if it converges or diverges
Transcribed Image Text: S 3
n=l
4n+7
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With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
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