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 5.19TI: The polynomial function h(t)=16t2+150 gives the height of a stone t seconds after it is dropped from...
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The polynomial function h(t)=−16t2+150 gives the height of a stone t seconds after it is dropped from a cliff that is 150 feet tall. Find the height after t=0 seconds (the initial height of the object).
Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.
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