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  • Algebra II - Polynomials ~1~ NJCTL.org

    Polynomial Functions

    NOTE: Some problems in this file are used with permission from the engageny.org website of the

    New York State Department of Education. Various files. Internet. Available from

    https://www.engageny.org/ccss-library. Accessed August, 2014.

    Properties of Exponents: Class Work

    Simplify the following expressions.

    1. (βˆ’4𝑔3β„Ž2π‘—βˆ’2)βˆ’3

    2. ( 4π‘˜3

    3π‘šπ‘›2 )

    2

    3. ( 3p7q3

    (2p2q2)3 )

    βˆ’2

    4. (5r3s4t2)(2r3sβˆ’3)4

    5. (3u2vβˆ’4)3(6u4v3)βˆ’2

    6. ( 8w2xβˆ’3y4z5

    12w3xβˆ’4y5zβˆ’6 )

    βˆ’3

    Properties of Exponents: Homework

    Simplify the following expressions.

    7. (βˆ’3π‘”βˆ’4β„Ž3π‘—βˆ’3)βˆ’4

    8. ( 4π‘˜4

    6π‘š3π‘›βˆ’4 )

    2

    9. ( 8p7q9

    (2p2q2)4 )

    βˆ’2

    10. 4(5r10s12t8)(2r4sβˆ’5)βˆ’3

    11. (6u6vβˆ’3)3(9u5vβˆ’6)βˆ’2

    12. ( 6wβˆ’3xβˆ’4y5z6

    15w3xβˆ’4y5zβˆ’6 )

    βˆ’2

    https://www.engageny.org/ccss-library

  • Algebra II - Polynomials ~2~ NJCTL.org

    Operations with Polynomials: Class Work

    Determine if each function is a polynomial function. If so, write it in standard form, name its degree, state its

    type based on degree and based on number of terms, and identify the leading coefficient.

    13. 2π‘₯2 + 3π‘₯2

    14. 4

    7 𝑦 βˆ’ 3𝑦2 + 3𝑦

    15. 5π‘Ž3 βˆ’ 2π‘Ž βˆ’ 4π‘Ž + 3

    16. 6π‘Ž2

    𝑏 βˆ’ 5π‘Žπ‘2 + 2π‘Žπ‘2

    17. (2π‘₯βˆ’2 βˆ’ 4) + (βˆ’5π‘₯βˆ’2 βˆ’ 3)

    Perform the indicated operations.

    18. (4g2 βˆ’ 2) βˆ’ (3g + 5) + (2g2 βˆ’ g)

    19. (6𝑑 βˆ’ 3𝑑2 + 4) βˆ’ (𝑑2 + 5𝑑 βˆ’ 9)

    20. (7π‘₯5 + 8π‘₯4 βˆ’ 3π‘₯) + (5π‘₯4 + 2π‘₯3 + 9π‘₯ βˆ’ 1)

    21. (βˆ’10π‘₯3 + 4π‘₯2 βˆ’ 5π‘₯ + 9) βˆ’ (2π‘₯3 βˆ’ 2π‘₯2 + π‘₯ + 12)

    22. The legs of an isosceles triangle are (3x2+ 4x +2) inches and the base is (4x-5) inches. Find the

    perimeter of the triangle.

    23. βˆ’2π‘Ž(4π‘Ž2𝑏 βˆ’ 3π‘Žπ‘2 βˆ’ 6π‘Žπ‘)

    24. 7π‘—π‘˜2(5𝑗3π‘˜ + 9𝑗2 βˆ’ 2π‘˜ + 10)

    25. (2x βˆ’ 3)(4x + 2)

    26. (𝑐2 βˆ’ 3)(𝑐 + 4)

    27. (m βˆ’ 3)(2m2 + 4m βˆ’ 5)

    28. (2𝑓 + 5)(6𝑓2 βˆ’ 4𝑓 + 1)

    29. (3t2 βˆ’ 2t + 9)(4t2 βˆ’ t + 1)

  • Algebra II - Polynomials ~3~ NJCTL.org

    30. The width of a rectangle is (5x+2) inches and the length is (6x-7) inches. Find the area of the rectangle.

    31. The radius of the base of a cylinder is (3x + 4) cm and the height is (7x + 2) cm. Find the volume of the

    cylinder (V = πœ‹π‘Ÿ2β„Ž).

    32. A rectangle of (2x) ft by (3x-1) ft is cut out of a large rectangle of (4x+1)ft by (2x+2)ft. What is area of the shape that remains?

    33. A pool that is 20ft by 30ft is going to have a deck of width x ft added all the way around the pool. Write an expression in simplified form for the area of the deck.

    Multiply and simplify:

    34. (𝑏 + 2)2

    35. (𝑐 βˆ’ 1)(𝑐 βˆ’ 1)

    36. (2𝑑 + 4𝑒)2

    37. (5𝑓 + 9)(5𝑓 βˆ’ 9)

    38. What is the area of a square with sides (3x+2) inches? Expand, using the Binomial Theorem:

    39. (2π‘₯ + 4𝑦)5

    40. (7π‘Ž + 𝑏)3

    41. (3π‘₯ βˆ’ 4𝑧)6

    42. (𝑦 βˆ’ 5𝑧)4

  • Algebra II - Polynomials ~4~ NJCTL.org

    Operations with Polynomials: Homework

    Determine if each function is a polynomial function. If so, write it in standard form, name its degree, state its

    type based on degree and based on number of terms, and identify the leading coefficient.

    43. √2π‘₯2 + 0.4π‘₯3

    44. 4

    7𝑦 βˆ’ 8𝑦2 + 9𝑦

    45. 11π‘Ž4 βˆ’ 2π‘Ž3 + 7π‘Ž2 βˆ’ 8π‘Ž + 9

    46. 6π‘Ž2

    11 βˆ’

    5π‘Ž

    9 + 2

    47. (2π‘₯ 2

    3 βˆ’ 4) + (βˆ’5π‘₯2 βˆ’ 3)

    Perform the indicated operations:

    48. (3n βˆ’ 13) βˆ’ (2n2 + 4n βˆ’ 6) βˆ’ (5𝑛 βˆ’ 4)

    49. (5g2 βˆ’ 4) βˆ’ (3g3 + 7) + (5g2 βˆ’ 5g)

    50. (βˆ’8π‘₯4 + 7π‘₯3 βˆ’ 3π‘₯ + 5) + (5π‘₯4 + 2π‘₯2 βˆ’ 16π‘₯ βˆ’ 21)

    51. (17π‘₯3 βˆ’ 9π‘₯2 + 5π‘₯ βˆ’ 18) βˆ’ (11π‘₯3 βˆ’ 2π‘₯2 βˆ’ 19π‘₯ + 15)

    52. The width of a rectangle is (5x2+6x +2) inches and the length is (6x-7) inches. Find the perimeter of the

    rectangle.

    53. 4π‘₯(3π‘₯2 βˆ’ 5π‘₯ βˆ’ 2)

    54. βˆ’6π‘Ž(3π‘Ž2𝑏 βˆ’ 5π‘Žπ‘2 βˆ’ 7𝑏)

    55. 8𝑗2π‘˜3(2𝑗3π‘˜ + 6𝑗2 βˆ’ 5π‘˜ + 11)

    56. (4x + 5)(6x + 1)

    57. (2𝑏 βˆ’ 9)(4𝑏 βˆ’ 2)

    58. (2𝑐2 βˆ’ 4)(3𝑐 + 2)

    59. (2m βˆ’ 5)(3m2 βˆ’ 6m βˆ’ 4)

    60. (3𝑓 + 4)(6𝑓2 βˆ’ 4𝑓 + 1)

    61. (2𝑝2 βˆ’ 5)(𝑝2 + 8𝑝 + 2)

    62. (5t2 βˆ’ 3t + 6)(3t2 βˆ’ 2t + 1)

  • Algebra II - Polynomials ~5~ NJCTL.org

    63. The width of a rectangle is (4x-3) inches and the length is (3x-5) inches. Find the area of the rectangle.

    64. The radius of the base of a cone is (9x - 3) cm and the height is (3x + 2) cm. Find the volume of the

    cylinder (V = 1

    3 πœ‹π‘Ÿ2β„Ž).

    65. A rectangle of (3x) ft by (5x-1) ft is cut out of a large rectangle of (6x+2)ft by (3x+4)ft. What is area of the

    shape that remains?

    66. A pool that is 25ft by 40ft is going to have a deck of width (x + 2) ft added all the way around the pool.

    Write an expression in simplified form for the area of the deck.

    Multiply and simplify: 67. (3π‘Ž βˆ’ 1)(3π‘Ž + 1)

    68. (𝑏 βˆ’ 2)2

    69. (𝑐 βˆ’ 1)(𝑐 + 1)

    70. (3𝑑 βˆ’ 5𝑒)2

    71. (5𝑓 + 9)(5𝑓 + 9)

    72. What is the area of a square with sides of (4x-6y) inches?

    Expand the following using the binomial Theorem:

    73. (2π‘Ž βˆ’ 𝑏)6

    74. (3π‘₯ + 2𝑦)3

    75. (5𝑦 βˆ’ 4𝑧)5

    76. (π‘Ž + 7𝑏)4

  • Algebra II - Polynomials ~6~ NJCTL.org

    Factoring I Classwork

    Factoring out the GCF

    77. 6x3y2 – 3x2y

    78. 10p3q – 15p3q2 – 5p2q2

    79. 7m3n3 – 7m3n2 + 14m3

    Factoring ax2 + bx + c

    80. x2 – 5x – 24

    81. m2 – mn – 6n2

    82. x2 – 2xy + y2

    83. a2 + ab – 12b2

    84. x2 – 6xy + 8y2

    85. 2x2 + 7x + 3

    86. 6x2 – x – 2

    87. 5a2 + 17a – 12

    88. 6m2 - 5mn + n2

    89. 6p2 + 37p + 6

    90. 4c2 + 20cd + 25d2

    Factoring I Homework

    Factoring out the GCF

    91. 8x3y – 4x2y2

    92. 8m3n3 – 4m2n3 – 32mn3

    93. -18p3q2 + 3pq

    Factoring ax2 + bx + c

    94. m2 – 2m – 24

    95. a2 – 13a + 12

    96. n2 + n – 6

    97. x2 – 10xy + 21y2

    98. x2 + 11xy + 18y2

    99. 6x2 – 5x + 1

    100. 15p2 – 22p – 5

    101. 10m2 + 13m – 3

    102. 12x2 – 7xy + y2

    103. 4p2 + 24p + 35

    104. 15m2 – 13mn + 2n2

    Spiral Review

    105. Simplify: 106. Multiply: 107. Divide 108. Evaluate, use x = 5:

    5 – 4 [(-2) – (-2)] 2 3

    4 βˆ™ 4

    2

    3 2

    3

    4 Γ· 4

    2

    3 -2(-6x – 9) + 4

  • Algebra II - Polynomials ~7~ NJCTL.org

    Factoring II Classwork

    Factoring a2 – b2, a3 – b3, a3 + b3

    109. a3 – 1

    110. 25x2 – 16y2

    111. 121a2 – 16b2

    112. 27x3 + 8y3

    113. a3b3 – c3

    114. 4x2y2 – 1

    Factoring by Grouping

    115. 2xy + 5x + 8y + 20

    116. 9mn – 3m – 15n + 5

    117. 2xy – 10x – 3y + 15

    118. 10rs – 25r + 6s – 15

    119. 10pq – 2p – 5q + 1

    120. 10mn + 5m + 6n + 3

    Mixed Factoring

    121. 3x3 – 12x2 + 36x

    122. 6m3 + 4m2 – 2m

    123. 3a3b – 48ab

    124. 54x4 + 2xy3

    125. x4y + 12x3y + 20x2y

    Factoring II Homework

    Factoring a2 – b2, a3 – b3, a3 + b3

    126. y3 + 27

    127. 64m3 – 1

    128. p2 – 36q2

    129. m2n2 – 4

    130. x2 + 16

    131. 8x3 – 27y3

    Factoring by Grouping

    132. 6mp – 2m – 15p + 5

    133. 6xy + 15x + 4y + 10

    134. 4rs – 4r + 3s – 3

    135. 6tr – 9t – 2r + 3

    136. 8mn + 4m + 6n + 3

    137. 3xy – 4x – 15y + 20

    Mixed Factoring

    138. 3m3 – 3mn2

    139. -6x3 – 28x2 + 10x

  • Algebra II - Polynomials ~8~ NJCTL.org

    140. 18a3b – 50ab

    141. x4y + 27xy

    142. -12r3 – 21r2 – 9r

    143. 2x2y2 – 2x2y – 2xy2 + 2xy

    Spiral Review

    144. Simplify: 145. Simplify: 146. Add: 147. Evaluate, use x = -3, y = 2

    8(-4) ο‚Έ (2)(-1) + (4)2 172 - (12 - 4)2 + 2 2 2

    7 + 5

    3

    5 -3x + 2y – xy + x

    Division of Polynomials: Class Work

    Simplify.

    148. 6x3βˆ’3x2+9x

    3x

    1

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