C Challenge

Factor by grouping.

41. y 3 + 11 y 2 − 4 y − 44 y cubed , plus , 11 y squared , minus 4 y minus 44
42. p 2 m + p 2 n 5 + q m + qn 5 p squared , m plus , p squared , n to the fifth , plus q m plus , qn to the fifth
43. 30 g 5 + 24 g 3 h − 35 g 2 h 2 − 28 h 3 30 g to the fifth , plus , 24 g cubed , h minus , 35 g squared . h squared , minus , 28 h cubed

44. Geometry The polynomial 2 π x 3 + 12 π x 2 + 18 π x 2 pi , x cubed , plus 12 pi , x squared , plus 18 pi x  represents the volume of a cylinder. The formula for the volume V of a cylinder with radius r and height h is V = π r 2 h . v equals pi , r squared , h .

    1. Factor 2 π x 3 + 12 π x 2 + 18 π x . 2 pi , x cubed , plus 12 pi , x squared , plus 18 pi x .
    2. Based on your answer to part (a), write an expression for a possible radius of the cylinder.

You can write the number 63 as 2 5 + 2 4 + 2 3 + 2 2 + 2 1 + 2 0 . 2 to the fifth , plus , 2 to the fourth , plus , 2 cubed , plus , 2 squared , plus , 2 to the first , plus , 2 to the , .  For Exercises 45 and 46, factor each expression by grouping. Then simplify the powers of 2 to write 63 as the product of two numbers.

45. ( 2 5 + 2 4 + 2 3 ) + ( 2 2 + 2 1 + 2 0 ) open , 2 to the fifth , plus , 2 to the fourth , plus , 2 cubed , close plus open , 2 squared , plus , 2 to the first , plus , 2 to the , close
46. ( 2 5 + 2 4 ) + ( 2 3 + 2 2 ) + ( 2 1 + 2 0 ) open , 2 to the fifth , plus , 2 to the fourth , close plus open , 2 cubed , plus , 2 squared , close plus open , 2 to the first , plus , 2 to the , close

Standardized Test Prep

SAT/ACT

47. What is 30 z 3 − 12 z 2 + 120 z − 48 30 z cubed , minus , 12 z squared , plus 120 z minus 48  factored completely?

    1. 2 ( 15 z 3 − 6 z 2 + 60 z − 24 ) 2 open , 15 z cubed , minus , 6 z squared , plus 60 z minus 24 close
    2. ( 6 z 2 + 24 ) ( 5 z − 2 ) open , 6 z squared , plus 24 close open 5 z minus 2 close
    3. 6 ( 5 z 3 − 2 z 2 + 20 z − 8 ) 6 open , 5 z cubed , minus , 2 z squared , plus 20 z minus 8 close
    4. 6 ( z 2 + 4 ) ( 5 z − 2 ) 6 open , z squared , plus 4 close open 5 z minus 2 close

48. What is the simplified form of 2 x 3 · x 8 ? 2 x cubed , middle dot , x to the eighth , question mark

    6. 2 x 11 2 x to the eleventh
    7. 8 x 11 8 x to the eleventh
    8. 2 x 24 2 x to the twenty fourth
    9. 8 x 24 8 x to the twenty fourth

49. Which equation represents the line with slope − 3 negative 3  that passes through (2, 5)?

    1. y = − 3 x + 17 y equals negative 3 x plus 17
    2. y = − 3 x + 11 y equals negative 3 x plus 11
    3. y = 4 x − 3 y equals 4 x minus 3
    4. y = x − 3 y equals x minus 3

50. What is the solution of the inequality 7 < − 2 x + 5 ? 7 less than negative 2 x plus 5 question mark

    6. x > − 1 x greater than negative 1
    7. x < − 1 x less than negative 1
    8. x > 1 x greater than 1
    9. x < 1 x less than 1
51. Short Response Factor 10 r 4 + 30 r 3 + 5 r 2 + 15 r 10 r to the fourth , plus , 30 r cubed , plus , 5 r squared , plus 15 r  completely. Show your work.

Mixed Review

See Lesson 8-7.

Factor each expression.

52. m 2 + 12 m + 36 m squared , plus 12 m plus 36
53. 64 x 2 − 144 x + 81 64 x squared , minus 144 x plus 81
54. 49 p 2 − 4 49 p squared , minus 4

See Lesson 4-6.

Use a mapping diagram to determine whether each relation is a function.

55. {(4, 3), (3, 4), (4, 7), (7, 4)}
56. {( − 1 , negative 1 comma  8), (1, 8), (3, 8), (5, 8)}
57. {(2, 7), (4, − 7 negative 7 ), (6, 7), (8, − 7 negative 7 )}

Get Ready! To prepare for Lesson 9-1, do Exercises 58–61.

See Lesson 5-3.

Use the slope and y-intercept to graph each equation.

58. y = 1 2 x + 3 y equals , 1 half , x plus 3
59. y = − 4 x − 1 y equals negative 4 x minus 1
60. y = 2 x − 3 y equals 2 x minus 3
61. y = − 5 3 x + 2 y equals negative , 5 thirds , x plus 2

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