{"id":130,"date":"2026-01-12T15:49:50","date_gmt":"2026-01-12T15:49:50","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/?post_type=chapter&p=130"},"modified":"2026-01-12T15:49:51","modified_gmt":"2026-01-12T15:49:51","slug":"power-and-polynomial-functions-get-stronger-answer-key","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/chapter\/power-and-polynomial-functions-get-stronger-answer-key\/","title":{"raw":"Power and Polynomial Functions: Get Stronger Answer Key","rendered":"Power and Polynomial Functions: Get Stronger Answer Key"},"content":{"raw":"

Introduction to Power and Polynomial Functions<\/span><\/h2>\r\n
    \r\n \t
  1. Power function<\/li>\r\n \t
  2. Neither<\/li>\r\n \t
  3. Neither<\/li>\r\n \t
  4. Degree = [latex]2[\/latex], Coefficient = [latex]-2[\/latex]<\/li>\r\n \t
  5. Degree = [latex]4[\/latex], Coefficient =[latex] -2[\/latex]<\/li>\r\n \t
  6. As [latex]x\\to\\infty, f(x)\\to\\infty[\/latex], as [latex]x\\to-\\infty, f(x)\\to\\infty[\/latex]<\/li>\r\n \t
  7. As [latex]x\\to-\\infty, f(x)\\to-\\infty[\/latex], as [latex]x\\to\\infty, f(x)\\to-\\infty[\/latex]<\/li>\r\n \t
  8. As [latex]x\\to-\\infty, f(x)\\to-\\infty[\/latex], as [latex]x\\to\\infty, f(x)\\to-\\infty[\/latex]<\/li>\r\n \t
  9. As [latex]x\\to\\infty, f(x)\\to\\infty[\/latex], as [latex]x\\to-\\infty, f(x)\\to-\\infty[\/latex]<\/li>\r\n \t
  10. [latex]y[\/latex]-intercept is [latex](0,12)[\/latex], [latex]x[\/latex]-intercepts are [latex](1,0)[\/latex]; [latex](-2,0)[\/latex]; and [latex](3,0)[\/latex].<\/li>\r\n \t
  11. [latex]y[\/latex]-intercept is [latex](0,-16)[\/latex], [latex]x[\/latex]-intercepts are [latex](2,0)[\/latex] and [latex](-2,0)[\/latex].<\/li>\r\n \t
  12. [latex]y[\/latex]-intercept is [latex](0,0)[\/latex], [latex]x[\/latex]-intercepts are [latex](0,0)[\/latex], ([latex]4,0)[\/latex], and [latex](-2,0)[\/latex].<\/li>\r\n \t
  13. [latex]3[\/latex]<\/li>\r\n \t
  14. [latex]5[\/latex]<\/li>\r\n \t
  15. [latex]3[\/latex]<\/li>\r\n \t
  16. [latex]5[\/latex]<\/li>\r\n \t
  17. Yes. Number of turning points is [latex]2[\/latex]. Least possible degree is [latex]3[\/latex].<\/li>\r\n \t
  18. Yes. Number of turning points is [latex]1[\/latex]. Least possible degree is [latex]2[\/latex].<\/li>\r\n \t
  19. Yes. Number of turning points is [latex]0[\/latex]. Least possible degree is [latex]1[\/latex].<\/li>\r\n \t
  20. Yes. Number of turning points is [latex]0[\/latex]. Least possible degree is [latex]1[\/latex].<\/li>\r\n \t
  21. [latex]V(m) = 8m^3 + 36m^2 + 54m + 27[\/latex]<\/li>\r\n \t
  22. [latex]V(x) = 4x^3 - 32x^2 + 64x[\/latex]<\/li>\r\n<\/ol>\r\n

    Graphs of Polynomial Functions<\/span><\/h2>\r\n
      \r\n \t
    1. [latex](-2,0), (3,0), (-5,0)[\/latex]<\/li>\r\n \t
    2. [latex](3,0), (-1,0), (0,0)[\/latex]<\/li>\r\n \t
    3. [latex](0,0), (-5,0), (2,0)[\/latex]<\/li>\r\n \t
    4. [latex](0,0), (-5,0), (4,0)[\/latex]<\/li>\r\n \t
    5. [latex](2,0), (-2,0), (-1,0)[\/latex]<\/li>\r\n \t
    6. [latex](-2,0), (2,0), (1\/2,0)[\/latex]<\/li>\r\n \t
    7. [latex](1,0), (-1,0)[\/latex]<\/li>\r\n \t
    8. [latex](0,0), (\\sqrt{3},0), (-\\sqrt{3},0)[\/latex]<\/li>\r\n \t
    9. [latex](0,0), (1,0), (-1,0), (2,0), (-2,0)[\/latex]<\/li>\r\n \t
    10. [latex]f(2)=-10[\/latex] and [latex]f(4)=28[\/latex]. Sign change confirms.<\/li>\r\n \t
    11. [latex]f(1)=3[\/latex] and [latex]f(3)=-77[\/latex]. Sign change confirms.<\/li>\r\n \t
    12. [latex]f(0.01)=1.000001[\/latex] and [latex]f(0.1)=-7.999[\/latex]. Sign change confirms.<\/li>\r\n \t
    13. [latex]0[\/latex] with multiplicity [latex]2[\/latex], [latex]-\\dfrac{3}{2}[\/latex] with multiplicity [latex]5[\/latex], [latex]4[\/latex] with multiplicity [latex]2[\/latex]<\/li>\r\n \t
    14. [latex]0[\/latex] with multiplicity [latex]2[\/latex], [latex]-2[\/latex] with multiplicity [latex]2[\/latex]<\/li>\r\n \t
    15. [latex]-\\dfrac{2}{3}[\/latex] with multiplicity [latex]5[\/latex], [latex]5[\/latex] with multiplicity [latex]2[\/latex]<\/li>\r\n \t
    16. [latex]0[\/latex] with multiplicity [latex]4[\/latex], [latex]2[\/latex] with multiplicity [latex]1[\/latex], [latex]-1[\/latex] with multiplicity [latex]1[\/latex]<\/li>\r\n \t
    17. [latex]\\dfrac{3}{2}[\/latex] with multiplicity [latex]2[\/latex], [latex]0[\/latex] with multiplicity [latex]3[\/latex]<\/li>\r\n \t
    18. [latex]0[\/latex] with multiplicity [latex]6[\/latex], [latex]\\dfrac{2}{3}[\/latex] with multiplicity [latex]2[\/latex]<\/li>\r\n \t
    19. [latex]x[\/latex]-intercepts, [latex](1,0)[\/latex] with multiplicity [latex]2[\/latex], [latex](-4,0)[\/latex] with multiplicity [latex]1[\/latex], [latex]y[\/latex]-intercept [latex](0,4)[\/latex]. As [latex]x\\to-\\infty, f(x)\\to-\\infty[\/latex], as [latex]x\\to\\infty, f(x)\\to\\infty[\/latex].\r\n\"Graph<\/li>\r\n \t
    20. [latex]x[\/latex]-intercepts [latex](3,0)[\/latex] with multiplicity [latex]3[\/latex], [latex](2,0)[\/latex] with multiplicity [latex]2[\/latex], [latex]y[\/latex]-intercept [latex](0,-108)[\/latex]. As [latex]x\\to-\\infty, f(x)\\to-\\infty[\/latex], as [latex]x\\to\\infty, f(x)\\to\\infty[\/latex].\r\n\"Graph<\/li>\r\n \t
    21. [latex]x[\/latex]-intercepts [latex](0,0)[\/latex], [latex](-2,0)[\/latex], [latex](4,0)[\/latex] with multiplicity [latex]1[\/latex], [latex]y[\/latex]-intercept [latex](0,0)[\/latex]. As [latex]x\\to-\\infty, f(x)\\to\\infty[\/latex], as [latex]x\\to\\infty, f(x)\\to-\\infty[\/latex].\r\n\"Graph<\/li>\r\n \t
    22. [latex]f(x)=-\\dfrac{2}{5}(x-3)(x+1)(x+3)[\/latex]<\/li>\r\n \t
    23. [latex]f(x)=\\dfrac{1}{4}(x+2)^2(x-3)[\/latex]<\/li>\r\n \t
    24. [latex]-4[\/latex], [latex]-2[\/latex], [latex]1[\/latex], [latex]3[\/latex] with multiplicity [latex]1[\/latex]<\/li>\r\n \t
    25. [latex]-2[\/latex], [latex]3[\/latex] each with multiplicity [latex]2[\/latex]<\/li>\r\n \t
    26. [latex]f(x)=-\\dfrac{2}{3}(x+2)(x-1)(x-3)[\/latex]<\/li>\r\n \t
    27. [latex]f(x)=\\dfrac{1}{3}(x-3)^2(x-1)^2(x+3)[\/latex]<\/li>\r\n \t
    28. [latex]f(x)=-15(x-1)^2(x-3)^3[\/latex]<\/li>\r\n \t
    29. [latex]f(x)=-2(x+3)(x+2)(x-1)[\/latex]<\/li>\r\n \t
    30. [latex]f(x)=-\\dfrac{3}{2}(2x-1)^2(x-6)(x+2)[\/latex]<\/li>\r\n<\/ol>\r\n

      Dividing Polynomials<\/span><\/h2>\r\n
        \r\n \t
      1. [latex]x+6+\\dfrac{5}{x-1}[\/latex], quotient: [latex]x+6[\/latex], remainder: [latex]5[\/latex]<\/li>\r\n \t
      2. [latex]3x+2[\/latex], quotient: [latex]3x+2[\/latex], remainder: [latex]0[\/latex]<\/li>\r\n \t
      3. [latex]x-5[\/latex], quotient: [latex]x-5[\/latex], remainder: [latex]0[\/latex]<\/li>\r\n \t
      4. [latex]2x-7+\\dfrac{16}{x-2}[\/latex], quotient: [latex]2x-7[\/latex], remainder: [latex]16[\/latex]<\/li>\r\n \t
      5. [latex]2x^2+2x+1+\\dfrac{10}{x-4}[\/latex]<\/li>\r\n \t
      6. [latex]2x^2-7x+1-\\dfrac{2}{2x+1}[\/latex]<\/li>\r\n \t
      7. [latex]3x^2-11x+34-\\dfrac{106}{x+3}[\/latex]<\/li>\r\n \t
      8. [latex]x^2+5x+1[\/latex]<\/li>\r\n \t
      9. [latex]4x^2-21x+84-\\dfrac{323}{x+4}[\/latex]<\/li>\r\n \t
      10. [latex]x^2-14x+49[\/latex]<\/li>\r\n \t
      11. Yes [latex](x-2)(3x^2-5)[\/latex]<\/li>\r\n \t
      12. Yes [latex](x-2)(4x^3+8x^2+x+2)[\/latex]<\/li>\r\n \t
      13. No<\/li>\r\n<\/ol>\r\n

        Zeros of Polynomial Functions<\/span><\/h2>\r\n
          \r\n \t
        1. [latex]-106[\/latex]<\/li>\r\n \t
        2. [latex]0[\/latex]<\/li>\r\n \t
        3. [latex]255[\/latex]<\/li>\r\n \t
        4. [latex]-1[\/latex]<\/li>\r\n \t
        5. [latex]-2[\/latex], [latex]1[\/latex], [latex]\\dfrac{1}{2}[\/latex]<\/li>\r\n \t
        6. [latex]-2[\/latex]<\/li>\r\n \t
        7. [latex]-3[\/latex]<\/li>\r\n \t
        8. [latex]-\\dfrac{5}{2}[\/latex], [latex]\\sqrt{6}[\/latex], [latex]-\\sqrt{6}[\/latex]<\/li>\r\n \t
        9. [latex]2[\/latex], [latex]-4[\/latex], [latex]-\\dfrac{3}{2}[\/latex]<\/li>\r\n \t
        10. [latex]4[\/latex], [latex]-4[\/latex], [latex]-5[\/latex]<\/li>\r\n \t
        11. [latex]5[\/latex], [latex]-3[\/latex], [latex]-\\dfrac{1}{2}[\/latex]<\/li>\r\n \t
        12. [latex]\\dfrac{1}{2}[\/latex], [latex]\\dfrac{1+\\sqrt{5}}{2}[\/latex], [latex]\\dfrac{1-\\sqrt{5}}{2}[\/latex]<\/li>\r\n \t
        13. [latex]\\dfrac{3}{2}[\/latex]<\/li>\r\n \t
        14. [latex]2[\/latex], [latex]3+2i[\/latex], [latex]3-2i[\/latex]<\/li>\r\n \t
        15. [latex]-\\dfrac{2}{3}[\/latex], [latex]1+2i[\/latex], [latex]1-2i[\/latex]<\/li>\r\n \t
        16. [latex]-\\dfrac{1}{2}[\/latex], [latex]1+4i[\/latex], [latex]1-4i[\/latex]<\/li>\r\n \t
        17. 1 positive, 1 negative\r\n\"Graph<\/li>\r\n \t
        18. 3 or 1 positive, 0 negative\r\n\"Graph<\/li>\r\n \t
        19. 0 positive, 3 or 1 negative\r\n\"Graph<\/li>\r\n \t
        20. 2 or 0 positive, 2 or 0 negative\r\n\"Graph<\/li>\r\n \t
        21. 2 or 0 positive, 2 or 0 negative\r\n\"Graph<\/li>\r\n \t
        22. [latex]\\pm5[\/latex], [latex]\\pm1[\/latex], [latex]\\pm\\dfrac{5}{2}[\/latex], [latex]\\pm\\dfrac{1}{2}[\/latex]<\/li>\r\n \t
        23. [latex]\\pm1[\/latex], [latex]\\pm\\dfrac{1}{2}[\/latex], [latex]\\pm\\dfrac{1}{3}[\/latex], [latex]\\pm\\dfrac{1}{6}[\/latex]<\/li>\r\n \t
        24. [latex]8[\/latex] by [latex]4[\/latex] by [latex]6[\/latex] inches<\/li>\r\n \t
        25. [latex]5.5[\/latex] by [latex]4.5[\/latex] by [latex]3.5[\/latex] inches<\/li>\r\n \t
        26. [latex]8[\/latex] by [latex]5[\/latex] by [latex]3[\/latex] inches<\/li>\r\n \t
        27. Radius = [latex]6[\/latex] meters, Height = [latex]2[\/latex] meters<\/li>\r\n \t
        28. Radius = [latex]2.5[\/latex] meters, Height = [latex]4.5[\/latex] meters<\/li>\r\n<\/ol>\r\n ","rendered":"

          Introduction to Power and Polynomial Functions<\/span><\/h2>\n
            \n
          1. Power function<\/li>\n
          2. Neither<\/li>\n
          3. Neither<\/li>\n
          4. Degree = [latex]2[\/latex], Coefficient = [latex]-2[\/latex]<\/li>\n
          5. Degree = [latex]4[\/latex], Coefficient =[latex]-2[\/latex]<\/li>\n
          6. As [latex]x\\to\\infty, f(x)\\to\\infty[\/latex], as [latex]x\\to-\\infty, f(x)\\to\\infty[\/latex]<\/li>\n
          7. As [latex]x\\to-\\infty, f(x)\\to-\\infty[\/latex], as [latex]x\\to\\infty, f(x)\\to-\\infty[\/latex]<\/li>\n
          8. As [latex]x\\to-\\infty, f(x)\\to-\\infty[\/latex], as [latex]x\\to\\infty, f(x)\\to-\\infty[\/latex]<\/li>\n
          9. As [latex]x\\to\\infty, f(x)\\to\\infty[\/latex], as [latex]x\\to-\\infty, f(x)\\to-\\infty[\/latex]<\/li>\n
          10. [latex]y[\/latex]-intercept is [latex](0,12)[\/latex], [latex]x[\/latex]-intercepts are [latex](1,0)[\/latex]; [latex](-2,0)[\/latex]; and [latex](3,0)[\/latex].<\/li>\n
          11. [latex]y[\/latex]-intercept is [latex](0,-16)[\/latex], [latex]x[\/latex]-intercepts are [latex](2,0)[\/latex] and [latex](-2,0)[\/latex].<\/li>\n
          12. [latex]y[\/latex]-intercept is [latex](0,0)[\/latex], [latex]x[\/latex]-intercepts are [latex](0,0)[\/latex], ([latex]4,0)[\/latex], and [latex](-2,0)[\/latex].<\/li>\n
          13. [latex]3[\/latex]<\/li>\n
          14. [latex]5[\/latex]<\/li>\n
          15. [latex]3[\/latex]<\/li>\n
          16. [latex]5[\/latex]<\/li>\n
          17. Yes. Number of turning points is [latex]2[\/latex]. Least possible degree is [latex]3[\/latex].<\/li>\n
          18. Yes. Number of turning points is [latex]1[\/latex]. Least possible degree is [latex]2[\/latex].<\/li>\n
          19. Yes. Number of turning points is [latex]0[\/latex]. Least possible degree is [latex]1[\/latex].<\/li>\n
          20. Yes. Number of turning points is [latex]0[\/latex]. Least possible degree is [latex]1[\/latex].<\/li>\n
          21. [latex]V(m) = 8m^3 + 36m^2 + 54m + 27[\/latex]<\/li>\n
          22. [latex]V(x) = 4x^3 - 32x^2 + 64x[\/latex]<\/li>\n<\/ol>\n

            Graphs of Polynomial Functions<\/span><\/h2>\n
              \n
            1. [latex](-2,0), (3,0), (-5,0)[\/latex]<\/li>\n
            2. [latex](3,0), (-1,0), (0,0)[\/latex]<\/li>\n
            3. [latex](0,0), (-5,0), (2,0)[\/latex]<\/li>\n
            4. [latex](0,0), (-5,0), (4,0)[\/latex]<\/li>\n
            5. [latex](2,0), (-2,0), (-1,0)[\/latex]<\/li>\n
            6. [latex](-2,0), (2,0), (1\/2,0)[\/latex]<\/li>\n
            7. [latex](1,0), (-1,0)[\/latex]<\/li>\n
            8. [latex](0,0), (\\sqrt{3},0), (-\\sqrt{3},0)[\/latex]<\/li>\n
            9. [latex](0,0), (1,0), (-1,0), (2,0), (-2,0)[\/latex]<\/li>\n
            10. [latex]f(2)=-10[\/latex] and [latex]f(4)=28[\/latex]. Sign change confirms.<\/li>\n
            11. [latex]f(1)=3[\/latex] and [latex]f(3)=-77[\/latex]. Sign change confirms.<\/li>\n
            12. [latex]f(0.01)=1.000001[\/latex] and [latex]f(0.1)=-7.999[\/latex]. Sign change confirms.<\/li>\n
            13. [latex]0[\/latex] with multiplicity [latex]2[\/latex], [latex]-\\dfrac{3}{2}[\/latex] with multiplicity [latex]5[\/latex], [latex]4[\/latex] with multiplicity [latex]2[\/latex]<\/li>\n
            14. [latex]0[\/latex] with multiplicity [latex]2[\/latex], [latex]-2[\/latex] with multiplicity [latex]2[\/latex]<\/li>\n
            15. [latex]-\\dfrac{2}{3}[\/latex] with multiplicity [latex]5[\/latex], [latex]5[\/latex] with multiplicity [latex]2[\/latex]<\/li>\n
            16. [latex]0[\/latex] with multiplicity [latex]4[\/latex], [latex]2[\/latex] with multiplicity [latex]1[\/latex], [latex]-1[\/latex] with multiplicity [latex]1[\/latex]<\/li>\n
            17. [latex]\\dfrac{3}{2}[\/latex] with multiplicity [latex]2[\/latex], [latex]0[\/latex] with multiplicity [latex]3[\/latex]<\/li>\n
            18. [latex]0[\/latex] with multiplicity [latex]6[\/latex], [latex]\\dfrac{2}{3}[\/latex] with multiplicity [latex]2[\/latex]<\/li>\n
            19. [latex]x[\/latex]-intercepts, [latex](1,0)[\/latex] with multiplicity [latex]2[\/latex], [latex](-4,0)[\/latex] with multiplicity [latex]1[\/latex], [latex]y[\/latex]-intercept [latex](0,4)[\/latex]. As [latex]x\\to-\\infty, f(x)\\to-\\infty[\/latex], as [latex]x\\to\\infty, f(x)\\to\\infty[\/latex].
              \n\"Graph<\/li>\n
            20. [latex]x[\/latex]-intercepts [latex](3,0)[\/latex] with multiplicity [latex]3[\/latex], [latex](2,0)[\/latex] with multiplicity [latex]2[\/latex], [latex]y[\/latex]-intercept [latex](0,-108)[\/latex]. As [latex]x\\to-\\infty, f(x)\\to-\\infty[\/latex], as [latex]x\\to\\infty, f(x)\\to\\infty[\/latex].
              \n\"Graph<\/li>\n
            21. [latex]x[\/latex]-intercepts [latex](0,0)[\/latex], [latex](-2,0)[\/latex], [latex](4,0)[\/latex] with multiplicity [latex]1[\/latex], [latex]y[\/latex]-intercept [latex](0,0)[\/latex]. As [latex]x\\to-\\infty, f(x)\\to\\infty[\/latex], as [latex]x\\to\\infty, f(x)\\to-\\infty[\/latex].
              \n\"Graph<\/li>\n
            22. [latex]f(x)=-\\dfrac{2}{5}(x-3)(x+1)(x+3)[\/latex]<\/li>\n
            23. [latex]f(x)=\\dfrac{1}{4}(x+2)^2(x-3)[\/latex]<\/li>\n
            24. [latex]-4[\/latex], [latex]-2[\/latex], [latex]1[\/latex], [latex]3[\/latex] with multiplicity [latex]1[\/latex]<\/li>\n
            25. [latex]-2[\/latex], [latex]3[\/latex] each with multiplicity [latex]2[\/latex]<\/li>\n
            26. [latex]f(x)=-\\dfrac{2}{3}(x+2)(x-1)(x-3)[\/latex]<\/li>\n
            27. [latex]f(x)=\\dfrac{1}{3}(x-3)^2(x-1)^2(x+3)[\/latex]<\/li>\n
            28. [latex]f(x)=-15(x-1)^2(x-3)^3[\/latex]<\/li>\n
            29. [latex]f(x)=-2(x+3)(x+2)(x-1)[\/latex]<\/li>\n
            30. [latex]f(x)=-\\dfrac{3}{2}(2x-1)^2(x-6)(x+2)[\/latex]<\/li>\n<\/ol>\n

              Dividing Polynomials<\/span><\/h2>\n
                \n
              1. [latex]x+6+\\dfrac{5}{x-1}[\/latex], quotient: [latex]x+6[\/latex], remainder: [latex]5[\/latex]<\/li>\n
              2. [latex]3x+2[\/latex], quotient: [latex]3x+2[\/latex], remainder: [latex]0[\/latex]<\/li>\n
              3. [latex]x-5[\/latex], quotient: [latex]x-5[\/latex], remainder: [latex]0[\/latex]<\/li>\n
              4. [latex]2x-7+\\dfrac{16}{x-2}[\/latex], quotient: [latex]2x-7[\/latex], remainder: [latex]16[\/latex]<\/li>\n
              5. [latex]2x^2+2x+1+\\dfrac{10}{x-4}[\/latex]<\/li>\n
              6. [latex]2x^2-7x+1-\\dfrac{2}{2x+1}[\/latex]<\/li>\n
              7. [latex]3x^2-11x+34-\\dfrac{106}{x+3}[\/latex]<\/li>\n
              8. [latex]x^2+5x+1[\/latex]<\/li>\n
              9. [latex]4x^2-21x+84-\\dfrac{323}{x+4}[\/latex]<\/li>\n
              10. [latex]x^2-14x+49[\/latex]<\/li>\n
              11. Yes [latex](x-2)(3x^2-5)[\/latex]<\/li>\n
              12. Yes [latex](x-2)(4x^3+8x^2+x+2)[\/latex]<\/li>\n
              13. No<\/li>\n<\/ol>\n

                Zeros of Polynomial Functions<\/span><\/h2>\n
                  \n
                1. [latex]-106[\/latex]<\/li>\n
                2. [latex]0[\/latex]<\/li>\n
                3. [latex]255[\/latex]<\/li>\n
                4. [latex]-1[\/latex]<\/li>\n
                5. [latex]-2[\/latex], [latex]1[\/latex], [latex]\\dfrac{1}{2}[\/latex]<\/li>\n
                6. [latex]-2[\/latex]<\/li>\n
                7. [latex]-3[\/latex]<\/li>\n
                8. [latex]-\\dfrac{5}{2}[\/latex], [latex]\\sqrt{6}[\/latex], [latex]-\\sqrt{6}[\/latex]<\/li>\n
                9. [latex]2[\/latex], [latex]-4[\/latex], [latex]-\\dfrac{3}{2}[\/latex]<\/li>\n
                10. [latex]4[\/latex], [latex]-4[\/latex], [latex]-5[\/latex]<\/li>\n
                11. [latex]5[\/latex], [latex]-3[\/latex], [latex]-\\dfrac{1}{2}[\/latex]<\/li>\n
                12. [latex]\\dfrac{1}{2}[\/latex], [latex]\\dfrac{1+\\sqrt{5}}{2}[\/latex], [latex]\\dfrac{1-\\sqrt{5}}{2}[\/latex]<\/li>\n
                13. [latex]\\dfrac{3}{2}[\/latex]<\/li>\n
                14. [latex]2[\/latex], [latex]3+2i[\/latex], [latex]3-2i[\/latex]<\/li>\n
                15. [latex]-\\dfrac{2}{3}[\/latex], [latex]1+2i[\/latex], [latex]1-2i[\/latex]<\/li>\n
                16. [latex]-\\dfrac{1}{2}[\/latex], [latex]1+4i[\/latex], [latex]1-4i[\/latex]<\/li>\n
                17. 1 positive, 1 negative
                  \n\"Graph<\/li>\n
                18. 3 or 1 positive, 0 negative
                  \n\"Graph<\/li>\n
                19. 0 positive, 3 or 1 negative
                  \n\"Graph<\/li>\n
                20. 2 or 0 positive, 2 or 0 negative
                  \n\"Graph<\/li>\n
                21. 2 or 0 positive, 2 or 0 negative
                  \n\"Graph<\/li>\n
                22. [latex]\\pm5[\/latex], [latex]\\pm1[\/latex], [latex]\\pm\\dfrac{5}{2}[\/latex], [latex]\\pm\\dfrac{1}{2}[\/latex]<\/li>\n
                23. [latex]\\pm1[\/latex], [latex]\\pm\\dfrac{1}{2}[\/latex], [latex]\\pm\\dfrac{1}{3}[\/latex], [latex]\\pm\\dfrac{1}{6}[\/latex]<\/li>\n
                24. [latex]8[\/latex] by [latex]4[\/latex] by [latex]6[\/latex] inches<\/li>\n
                25. [latex]5.5[\/latex] by [latex]4.5[\/latex] by [latex]3.5[\/latex] inches<\/li>\n
                26. [latex]8[\/latex] by [latex]5[\/latex] by [latex]3[\/latex] inches<\/li>\n
                27. Radius = [latex]6[\/latex] meters, Height = [latex]2[\/latex] meters<\/li>\n
                28. Radius = [latex]2.5[\/latex] meters, Height = [latex]4.5[\/latex] meters<\/li>\n<\/ol>\n

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