{"id":1340,"date":"2015-11-12T18:35:30","date_gmt":"2015-11-12T18:35:30","guid":{"rendered":"https:\/\/courses.candelalearning.com\/collegealgebra1xmaster\/?post_type=chapter&p=1340"},"modified":"2017-03-31T22:44:14","modified_gmt":"2017-03-31T22:44:14","slug":"section-exercises-47","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/chapter\/section-exercises-47\/","title":{"raw":"Section Exercises","rendered":"Section Exercises"},"content":{"raw":"

1. What is the difference between an x<\/em>-intercept and a zero of a polynomial function f<\/em>?\r\n\r\n2.\u00a0If a polynomial function of degree n<\/em>\u00a0has n<\/em>\u00a0distinct zeros, what do you know about the graph of the function?\r\n\r\n3. Explain how the Intermediate Value Theorem can assist us in finding a zero of a function.\r\n\r\n4.\u00a0Explain how the factored form of the polynomial helps us in graphing it.\r\n\r\n5. If the graph of a polynomial just touches the x<\/em>-axis and then changes direction, what can we conclude about the factored form of the polynomial?\r\n\r\nFor the following exercises, find the x<\/em>-\u00a0or t<\/em>-intercepts of the polynomial functions.\r\n\r\n6. [latex]C\\left(t\\right)=2\\left(t - 4\\right)\\left(t+1\\right)\\left(t - 6\\right)[\/latex]\r\n\r\n7. [latex]C\\left(t\\right)=3\\left(t+2\\right)\\left(t - 3\\right)\\left(t+5\\right)[\/latex]\r\n\r\n8.\u00a0[latex]C\\left(t\\right)=4t{\\left(t - 2\\right)}^{2}\\left(t+1\\right)[\/latex]\r\n\r\n9. [latex]C\\left(t\\right)=2t\\left(t - 3\\right){\\left(t+1\\right)}^{2}[\/latex]\r\n\r\n10.\u00a0[latex]C\\left(t\\right)=2{t}^{4}-8{t}^{3}+6{t}^{2}[\/latex]\r\n\r\n11. [latex]C\\left(t\\right)=4{t}^{4}+12{t}^{3}-40{t}^{2}[\/latex]\r\n\r\n12.\u00a0[latex]f\\left(x\\right)={x}^{4}-{x}^{2}[\/latex]\r\n\r\n13. [latex]f\\left(x\\right)={x}^{3}+{x}^{2}-20x[\/latex]\r\n\r\n14.\u00a0[latex]f\\left(x\\right)={x}^{3}+6{x}^{2}-7x[\/latex]\r\n\r\n15. [latex]f\\left(x\\right)={x}^{3}+{x}^{2}-4x - 4[\/latex]\r\n\r\n16.\u00a0[latex]f\\left(x\\right)={x}^{3}+2{x}^{2}-9x - 18[\/latex]\r\n\r\n17. [latex]f\\left(x\\right)=2{x}^{3}-{x}^{2}-8x+4[\/latex]\r\n\r\n18.\u00a0[latex]f\\left(x\\right)={x}^{6}-7{x}^{3}-8[\/latex]\r\n\r\n19. [latex]f\\left(x\\right)=2{x}^{4}+6{x}^{2}-8[\/latex]\r\n\r\n20.\u00a0[latex]f\\left(x\\right)={x}^{3}-3{x}^{2}-x+3[\/latex]\r\n\r\n21. [latex]f\\left(x\\right)={x}^{6}-2{x}^{4}-3{x}^{2}[\/latex]\r\n\r\n22.\u00a0[latex]f\\left(x\\right)={x}^{6}-3{x}^{4}-4{x}^{2}[\/latex]\r\n\r\n23. [latex]f\\left(x\\right)={x}^{5}-5{x}^{3}+4x[\/latex]\r\n\r\nFor the following exercises, use the Intermediate Value Theorem to confirm that the given polynomial has at least one zero within the given interval.\r\n\r\n24. [latex]f\\left(x\\right)={x}^{3}-9x[\/latex],\u00a0between [latex]x=-4[\/latex]\u00a0and [latex]x=-2[\/latex].\r\n\r\n25. [latex]f\\left(x\\right)={x}^{3}-9x[\/latex],\u00a0between [latex]x=2[\/latex]\u00a0and [latex]x=4[\/latex].\r\n\r\n26. [latex]f\\left(x\\right)={x}^{5}-2x[\/latex],\u00a0between [latex]x=1[\/latex]\u00a0and [latex]x=2[\/latex].\r\n\r\n27. [latex]f\\left(x\\right)=-{x}^{4}+4[\/latex],\u00a0between [latex]x=1[\/latex]\u00a0and [latex]x=3[\/latex].\r\n\r\n28.\u00a0[latex]f\\left(x\\right)=-2{x}^{3}-x[\/latex],\u00a0between [latex]x=-1[\/latex]\u00a0and [latex]x=1[\/latex].\r\n\r\n29. [latex]f\\left(x\\right)={x}^{3}-100x+2[\/latex],\u00a0between [latex]x=0.01[\/latex]\u00a0and [latex]x=0.1[\/latex]\r\n\r\nFor the following exercises, find the zeros and give the multiplicity of each.\r\n\r\n30. [latex]f\\left(x\\right)={\\left(x+2\\right)}^{3}{\\left(x - 3\\right)}^{2}[\/latex]\r\n\r\n31. [latex]f\\left(x\\right)={x}^{2}{\\left(2x+3\\right)}^{5}{\\left(x - 4\\right)}^{2}[\/latex]\r\n\r\n32.\u00a0[latex]f\\left(x\\right)={x}^{3}{\\left(x - 1\\right)}^{3}\\left(x+2\\right)[\/latex]\r\n\r\n33. [latex]f\\left(x\\right)={x}^{2}\\left({x}^{2}+4x+4\\right)[\/latex]\r\n\r\n34.\u00a0[latex]f\\left(x\\right)={\\left(2x+1\\right)}^{3}\\left(9{x}^{2}-6x+1\\right)[\/latex]\r\n\r\n35. [latex]f\\left(x\\right)={\\left(3x+2\\right)}^{5}\\left({x}^{2}-10x+25\\right)[\/latex]\r\n\r\n36.\u00a0[latex]f\\left(x\\right)=x\\left(4{x}^{2}-12x+9\\right)\\left({x}^{2}+8x+16\\right)[\/latex]\r\n\r\n37. [latex]f\\left(x\\right)={x}^{6}-{x}^{5}-2{x}^{4}[\/latex]\r\n\r\n38.\u00a0[latex]f\\left(x\\right)=3{x}^{4}+6{x}^{3}+3{x}^{2}[\/latex]\r\n\r\n39. [latex]f\\left(x\\right)=4{x}^{5}-12{x}^{4}+9{x}^{3}[\/latex]\r\n\r\n40.\u00a0[latex]f\\left(x\\right)=2{x}^{4}\\left({x}^{3}-4{x}^{2}+4x\\right)[\/latex]\r\n\r\n41. [latex]f\\left(x\\right)=4{x}^{4}\\left(9{x}^{4}-12{x}^{3}+4{x}^{2}\\right)[\/latex]\r\n\r\nFor the following exercises, graph the polynomial functions. Note x-<\/em>\u00a0and y<\/em>-intercepts, multiplicity, and end behavior.\r\n\r\n42. [latex]f\\left(x\\right)={\\left(x+3\\right)}^{2}\\left(x - 2\\right)[\/latex]\r\n\r\n43. [latex]g\\left(x\\right)=\\left(x+4\\right){\\left(x - 1\\right)}^{2}[\/latex]\r\n\r\n44.\u00a0[latex]h\\left(x\\right)={\\left(x - 1\\right)}^{3}{\\left(x+3\\right)}^{2}[\/latex]\r\n\r\n45. [latex]k\\left(x\\right)={\\left(x - 3\\right)}^{3}{\\left(x - 2\\right)}^{2}[\/latex]\r\n\r\n46. [latex]m\\left(x\\right)=-2x\\left(x - 1\\right)\\left(x+3\\right)[\/latex]\r\n\r\n47. [latex]n\\left(x\\right)=-3x\\left(x+2\\right)\\left(x - 4\\right)[\/latex]\r\n\r\nFor the following exercises, use the graphs to write the formula for a polynomial function of least degree.\r\n\r\n48.\r\n\"Graph\r\n\r\n49.\r\n\"Graph\r\n50.\r\n\"Graph\r\n\r\n51.\r\n\"Graph\r\n\r\n52.\r\n\"Graph\r\nFor the following exercises, use the graph to identify zeros and multiplicity.\r\n\r\n53.\r\n\"Graph\r\n54.\r\n\"Graph\r\n\r\n55.\r\n\"Graph\r\n\r\n56.\r\n\"Graph\r\nFor the following exercises, use the given information about the polynomial graph to write the equation.\r\n\r\n57. Degree 3. Zeros at x\u00a0<\/em>= \u20132, x\u00a0<\/em>= 1, and x\u00a0<\/em>= 3. y<\/em>-intercept at [latex]\\left(0,-4\\right)[\/latex].\r\n\r\n58.\u00a0Degree 3. Zeros at [latex]x=\\text{-5,}[\/latex] [latex]x=-2[\/latex], and [latex]x=1[\/latex]. y<\/em>-intercept at [latex]\\left(0,6\\right)[\/latex]\r\n\r\n59. Degree 5. Roots of multiplicity 2 at [latex]x=3[\/latex]\u00a0and [latex]x=1[\/latex], and a root of multiplicity 1 at [latex]x=-3[\/latex]. y<\/em>-intercept at [latex]\\left(0,9\\right)[\/latex]\r\n\r\n60.\u00a0Degree 4. Root of multiplicity 2 at [latex]x=4[\/latex], and a roots of multiplicity 1 at [latex]x=1[\/latex] and [latex]x=-2[\/latex]. y<\/em>-intercept at [latex]\\left(0,-3\\right)[\/latex].\r\n\r\n61. Degree 5. Double zero at [latex]x=1[\/latex], and triple zero at [latex]x=3[\/latex]. Passes through the point [latex]\\left(2,15\\right)[\/latex].\r\n\r\n62.\u00a0Degree 3. Zeros at [latex]x=4[\/latex], [latex]x=3[\/latex], and [latex]x=2[\/latex]. y<\/em>-intercept at [latex]\\left(0,-24\\right)[\/latex].\r\n\r\n63. Degree 3. Zeros at [latex]x=-3[\/latex], [latex]x=-2[\/latex]\u00a0and [latex]x=1[\/latex]. y<\/em>-intercept at [latex]\\left(0,12\\right)[\/latex].\r\n\r\n64.\u00a0Degree 5. Roots of multiplicity 2 at [latex]x=-3[\/latex]\u00a0and [latex]x=2[\/latex]\u00a0and a root of multiplicity 1 at [latex]x=-2[\/latex].\u00a0y<\/em>-intercept at [latex]\\left(0, 4\\right)[\/latex].\r\n\r\n65. Degree 4. Roots of multiplicity 2 at [latex]x=\\frac{1}{2}[\/latex] and roots of multiplicity 1 at [latex]x=6[\/latex] and [latex]x=-2[\/latex].\u00a0y<\/em>-intercept at [latex]\\left(0,18\\right)[\/latex].\r\n\r\n66.\u00a0Double zero at [latex]x=-3[\/latex]\u00a0and triple zero at [latex]x=0[\/latex].\u00a0Passes through the point [latex]\\left(1,32\\right)[\/latex].\r\n\r\nFor the following exercises, use a calculator to approximate local minima and maxima or the global minimum and maximum.\r\n\r\n67. [latex]f\\left(x\\right)={x}^{3}-x - 1[\/latex]\r\n\r\n68.\u00a0[latex]f\\left(x\\right)=2{x}^{3}-3x - 1[\/latex]\r\n\r\n69. [latex]f\\left(x\\right)={x}^{4}+x[\/latex]\r\n\r\n70.\u00a0[latex]f\\left(x\\right)=-{x}^{4}+3x - 2[\/latex]\r\n\r\n71. [latex]f\\left(x\\right)={x}^{4}-{x}^{3}+1[\/latex]\r\n\r\nFor the following exercises, use the graphs to write a polynomial function of least degree.\r\n\r\n72.\r\n\"Graph\r\n\r\n73.\r\n\"Graph\r\n\r\n74.\r\n\"Graph\r\n\r\nFor the following exercises, write the polynomial function that models the given situation.\r\n\r\n75. A rectangle has a length of 10 units and a width of 8 units. Squares of x<\/em>\u00a0by x<\/em>\u00a0units are cut out of each corner, and then the sides are folded up to create an open box. Express the volume of the box as a polynomial function in terms of x<\/em>.\r\n\r\n76.\u00a0Consider the same rectangle of the preceding problem. Squares of 2x<\/em>\u00a0by 2x<\/em>\u00a0units are cut out of each corner. Express the volume of the box as a polynomial in terms of x<\/em>.\r\n\r\n77. A square has sides of 12 units. Squares [latex]x+1[\/latex]\u00a0by [latex]x+1[\/latex]\u00a0units are cut out of each corner, and then the sides are folded up to create an open box. Express the volume of the box as a function in terms of x<\/em>.\r\n\r\n78.\u00a0A cylinder has a radius of [latex]x+2[\/latex]\u00a0units and a height of 3 units greater. Express the volume of the cylinder as a polynomial function.\r\n\r\n79. A right circular cone has a radius of [latex]3x+6[\/latex]\u00a0and a height 3 units less. Express the volume of the cone as a polynomial function. The volume of a cone is [latex]V=\\frac{1}{3}\\pi {r}^{2}h[\/latex]\u00a0for radius r<\/em>\u00a0and height h<\/em>.<\/p>","rendered":"

1. What is the difference between an x<\/em>-intercept and a zero of a polynomial function f<\/em>?<\/p>\n

2.\u00a0If a polynomial function of degree n<\/em>\u00a0has n<\/em>\u00a0distinct zeros, what do you know about the graph of the function?<\/p>\n

3. Explain how the Intermediate Value Theorem can assist us in finding a zero of a function.<\/p>\n

4.\u00a0Explain how the factored form of the polynomial helps us in graphing it.<\/p>\n

5. If the graph of a polynomial just touches the x<\/em>-axis and then changes direction, what can we conclude about the factored form of the polynomial?<\/p>\n

For the following exercises, find the x<\/em>–\u00a0or t<\/em>-intercepts of the polynomial functions.<\/p>\n

6. [latex]C\\left(t\\right)=2\\left(t - 4\\right)\\left(t+1\\right)\\left(t - 6\\right)[\/latex]<\/p>\n

7. [latex]C\\left(t\\right)=3\\left(t+2\\right)\\left(t - 3\\right)\\left(t+5\\right)[\/latex]<\/p>\n

8.\u00a0[latex]C\\left(t\\right)=4t{\\left(t - 2\\right)}^{2}\\left(t+1\\right)[\/latex]<\/p>\n

9. [latex]C\\left(t\\right)=2t\\left(t - 3\\right){\\left(t+1\\right)}^{2}[\/latex]<\/p>\n

10.\u00a0[latex]C\\left(t\\right)=2{t}^{4}-8{t}^{3}+6{t}^{2}[\/latex]<\/p>\n

11. [latex]C\\left(t\\right)=4{t}^{4}+12{t}^{3}-40{t}^{2}[\/latex]<\/p>\n

12.\u00a0[latex]f\\left(x\\right)={x}^{4}-{x}^{2}[\/latex]<\/p>\n

13. [latex]f\\left(x\\right)={x}^{3}+{x}^{2}-20x[\/latex]<\/p>\n

14.\u00a0[latex]f\\left(x\\right)={x}^{3}+6{x}^{2}-7x[\/latex]<\/p>\n

15. [latex]f\\left(x\\right)={x}^{3}+{x}^{2}-4x - 4[\/latex]<\/p>\n

16.\u00a0[latex]f\\left(x\\right)={x}^{3}+2{x}^{2}-9x - 18[\/latex]<\/p>\n

17. [latex]f\\left(x\\right)=2{x}^{3}-{x}^{2}-8x+4[\/latex]<\/p>\n

18.\u00a0[latex]f\\left(x\\right)={x}^{6}-7{x}^{3}-8[\/latex]<\/p>\n

19. [latex]f\\left(x\\right)=2{x}^{4}+6{x}^{2}-8[\/latex]<\/p>\n

20.\u00a0[latex]f\\left(x\\right)={x}^{3}-3{x}^{2}-x+3[\/latex]<\/p>\n

21. [latex]f\\left(x\\right)={x}^{6}-2{x}^{4}-3{x}^{2}[\/latex]<\/p>\n

22.\u00a0[latex]f\\left(x\\right)={x}^{6}-3{x}^{4}-4{x}^{2}[\/latex]<\/p>\n

23. [latex]f\\left(x\\right)={x}^{5}-5{x}^{3}+4x[\/latex]<\/p>\n

For the following exercises, use the Intermediate Value Theorem to confirm that the given polynomial has at least one zero within the given interval.<\/p>\n

24. [latex]f\\left(x\\right)={x}^{3}-9x[\/latex],\u00a0between [latex]x=-4[\/latex]\u00a0and [latex]x=-2[\/latex].<\/p>\n

25. [latex]f\\left(x\\right)={x}^{3}-9x[\/latex],\u00a0between [latex]x=2[\/latex]\u00a0and [latex]x=4[\/latex].<\/p>\n

26. [latex]f\\left(x\\right)={x}^{5}-2x[\/latex],\u00a0between [latex]x=1[\/latex]\u00a0and [latex]x=2[\/latex].<\/p>\n

27. [latex]f\\left(x\\right)=-{x}^{4}+4[\/latex],\u00a0between [latex]x=1[\/latex]\u00a0and [latex]x=3[\/latex].<\/p>\n

28.\u00a0[latex]f\\left(x\\right)=-2{x}^{3}-x[\/latex],\u00a0between [latex]x=-1[\/latex]\u00a0and [latex]x=1[\/latex].<\/p>\n

29. [latex]f\\left(x\\right)={x}^{3}-100x+2[\/latex],\u00a0between [latex]x=0.01[\/latex]\u00a0and [latex]x=0.1[\/latex]<\/p>\n

For the following exercises, find the zeros and give the multiplicity of each.<\/p>\n

30. [latex]f\\left(x\\right)={\\left(x+2\\right)}^{3}{\\left(x - 3\\right)}^{2}[\/latex]<\/p>\n

31. [latex]f\\left(x\\right)={x}^{2}{\\left(2x+3\\right)}^{5}{\\left(x - 4\\right)}^{2}[\/latex]<\/p>\n

32.\u00a0[latex]f\\left(x\\right)={x}^{3}{\\left(x - 1\\right)}^{3}\\left(x+2\\right)[\/latex]<\/p>\n

33. [latex]f\\left(x\\right)={x}^{2}\\left({x}^{2}+4x+4\\right)[\/latex]<\/p>\n

34.\u00a0[latex]f\\left(x\\right)={\\left(2x+1\\right)}^{3}\\left(9{x}^{2}-6x+1\\right)[\/latex]<\/p>\n

35. [latex]f\\left(x\\right)={\\left(3x+2\\right)}^{5}\\left({x}^{2}-10x+25\\right)[\/latex]<\/p>\n

36.\u00a0[latex]f\\left(x\\right)=x\\left(4{x}^{2}-12x+9\\right)\\left({x}^{2}+8x+16\\right)[\/latex]<\/p>\n

37. [latex]f\\left(x\\right)={x}^{6}-{x}^{5}-2{x}^{4}[\/latex]<\/p>\n

38.\u00a0[latex]f\\left(x\\right)=3{x}^{4}+6{x}^{3}+3{x}^{2}[\/latex]<\/p>\n

39. [latex]f\\left(x\\right)=4{x}^{5}-12{x}^{4}+9{x}^{3}[\/latex]<\/p>\n

40.\u00a0[latex]f\\left(x\\right)=2{x}^{4}\\left({x}^{3}-4{x}^{2}+4x\\right)[\/latex]<\/p>\n

41. [latex]f\\left(x\\right)=4{x}^{4}\\left(9{x}^{4}-12{x}^{3}+4{x}^{2}\\right)[\/latex]<\/p>\n

For the following exercises, graph the polynomial functions. Note x-<\/em>\u00a0and y<\/em>-intercepts, multiplicity, and end behavior.<\/p>\n

42. [latex]f\\left(x\\right)={\\left(x+3\\right)}^{2}\\left(x - 2\\right)[\/latex]<\/p>\n

43. [latex]g\\left(x\\right)=\\left(x+4\\right){\\left(x - 1\\right)}^{2}[\/latex]<\/p>\n

44.\u00a0[latex]h\\left(x\\right)={\\left(x - 1\\right)}^{3}{\\left(x+3\\right)}^{2}[\/latex]<\/p>\n

45. [latex]k\\left(x\\right)={\\left(x - 3\\right)}^{3}{\\left(x - 2\\right)}^{2}[\/latex]<\/p>\n

46. [latex]m\\left(x\\right)=-2x\\left(x - 1\\right)\\left(x+3\\right)[\/latex]<\/p>\n

47. [latex]n\\left(x\\right)=-3x\\left(x+2\\right)\\left(x - 4\\right)[\/latex]<\/p>\n

For the following exercises, use the graphs to write the formula for a polynomial function of least degree.<\/p>\n

48.
\n\"Graph<\/p>\n

49.
\n\"Graph
\n50.
\n\"Graph<\/p>\n

51.
\n\"Graph<\/p>\n

52.
\n\"Graph
\nFor the following exercises, use the graph to identify zeros and multiplicity.<\/p>\n

53.
\n\"Graph
\n54.
\n\"Graph<\/p>\n

55.
\n\"Graph<\/p>\n

56.
\n\"Graph
\nFor the following exercises, use the given information about the polynomial graph to write the equation.<\/p>\n

57. Degree 3. Zeros at x\u00a0<\/em>= \u20132, x\u00a0<\/em>= 1, and x\u00a0<\/em>= 3. y<\/em>-intercept at [latex]\\left(0,-4\\right)[\/latex].<\/p>\n

58.\u00a0Degree 3. Zeros at [latex]x=\\text{-5,}[\/latex] [latex]x=-2[\/latex], and [latex]x=1[\/latex]. y<\/em>-intercept at [latex]\\left(0,6\\right)[\/latex]<\/p>\n

59. Degree 5. Roots of multiplicity 2 at [latex]x=3[\/latex]\u00a0and [latex]x=1[\/latex], and a root of multiplicity 1 at [latex]x=-3[\/latex]. y<\/em>-intercept at [latex]\\left(0,9\\right)[\/latex]<\/p>\n

60.\u00a0Degree 4. Root of multiplicity 2 at [latex]x=4[\/latex], and a roots of multiplicity 1 at [latex]x=1[\/latex] and [latex]x=-2[\/latex]. y<\/em>-intercept at [latex]\\left(0,-3\\right)[\/latex].<\/p>\n

61. Degree 5. Double zero at [latex]x=1[\/latex], and triple zero at [latex]x=3[\/latex]. Passes through the point [latex]\\left(2,15\\right)[\/latex].<\/p>\n

62.\u00a0Degree 3. Zeros at [latex]x=4[\/latex], [latex]x=3[\/latex], and [latex]x=2[\/latex]. y<\/em>-intercept at [latex]\\left(0,-24\\right)[\/latex].<\/p>\n

63. Degree 3. Zeros at [latex]x=-3[\/latex], [latex]x=-2[\/latex]\u00a0and [latex]x=1[\/latex]. y<\/em>-intercept at [latex]\\left(0,12\\right)[\/latex].<\/p>\n

64.\u00a0Degree 5. Roots of multiplicity 2 at [latex]x=-3[\/latex]\u00a0and [latex]x=2[\/latex]\u00a0and a root of multiplicity 1 at [latex]x=-2[\/latex].\u00a0y<\/em>-intercept at [latex]\\left(0, 4\\right)[\/latex].<\/p>\n

65. Degree 4. Roots of multiplicity 2 at [latex]x=\\frac{1}{2}[\/latex] and roots of multiplicity 1 at [latex]x=6[\/latex] and [latex]x=-2[\/latex].\u00a0y<\/em>-intercept at [latex]\\left(0,18\\right)[\/latex].<\/p>\n

66.\u00a0Double zero at [latex]x=-3[\/latex]\u00a0and triple zero at [latex]x=0[\/latex].\u00a0Passes through the point [latex]\\left(1,32\\right)[\/latex].<\/p>\n

For the following exercises, use a calculator to approximate local minima and maxima or the global minimum and maximum.<\/p>\n

67. [latex]f\\left(x\\right)={x}^{3}-x - 1[\/latex]<\/p>\n

68.\u00a0[latex]f\\left(x\\right)=2{x}^{3}-3x - 1[\/latex]<\/p>\n

69. [latex]f\\left(x\\right)={x}^{4}+x[\/latex]<\/p>\n

70.\u00a0[latex]f\\left(x\\right)=-{x}^{4}+3x - 2[\/latex]<\/p>\n

71. [latex]f\\left(x\\right)={x}^{4}-{x}^{3}+1[\/latex]<\/p>\n

For the following exercises, use the graphs to write a polynomial function of least degree.<\/p>\n

72.
\n\"Graph<\/p>\n

73.
\n\"Graph<\/p>\n

74.
\n\"Graph<\/p>\n

For the following exercises, write the polynomial function that models the given situation.<\/p>\n

75. A rectangle has a length of 10 units and a width of 8 units. Squares of x<\/em>\u00a0by x<\/em>\u00a0units are cut out of each corner, and then the sides are folded up to create an open box. Express the volume of the box as a polynomial function in terms of x<\/em>.<\/p>\n

76.\u00a0Consider the same rectangle of the preceding problem. Squares of 2x<\/em>\u00a0by 2x<\/em>\u00a0units are cut out of each corner. Express the volume of the box as a polynomial in terms of x<\/em>.<\/p>\n

77. A square has sides of 12 units. Squares [latex]x+1[\/latex]\u00a0by [latex]x+1[\/latex]\u00a0units are cut out of each corner, and then the sides are folded up to create an open box. Express the volume of the box as a function in terms of x<\/em>.<\/p>\n

78.\u00a0A cylinder has a radius of [latex]x+2[\/latex]\u00a0units and a height of 3 units greater. Express the volume of the cylinder as a polynomial function.<\/p>\n

79. A right circular cone has a radius of [latex]3x+6[\/latex]\u00a0and a height 3 units less. Express the volume of the cone as a polynomial function. The volume of a cone is [latex]V=\\frac{1}{3}\\pi {r}^{2}h[\/latex]\u00a0for radius r<\/em>\u00a0and height h<\/em>.<\/p>\n\n\t\t\t

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