C Challenge

55. Find a fourth-degree polynomial function with zeros 1 , − 1 , i , 1 comma negative 1 comma i comma  and − i . negative i .  Write the function in factored form.
56. 1. Compare the graphs of y = ( x + 1 ) ( x + 2 ) ( x + 3 ) y equals open x plus 1 close open x plus 2 close open x plus 3 close  and y = ( x − 1 ) ( x − 2 ) ( x − 3 ) . y equals open x minus 1 close open x minus 2 close open x minus 3 close .  What transformation could you use to describe the change from one graph to the other?
    2. Compare the graphs of y = ( x + 1 ) ( x + 3 ) ( x + 7 ) y equals open x plus 1 close open x plus 3 close open x plus 7 close  and y = ( x − 1 ) ( x − 3 ) ( x − 7 ) . y equals open x minus 1 close open x minus 3 close open x minus 7 close .  Does the transformation that you chose in part (a) still hold true? Explain.
    3. Make a Conjecture What transformation could you use to describe the effect of changing the signs of the zeros of a polynomial function?

Standardized Test Prep

SAT/ACT

57. The three most frequent letters in the English language are E, T, and A. They represent, on average, 30% of all letters. The most frequent letter, E, is 4% more frequent than the second most frequent letter, T. The combined frequency of T and A is 4% greater than the frequency of E. Approximately how many E's can you expect to encounter in a 500-letter paragraph?

    1. 49
    2. 65
    3. 72
    4. 88
58. Which expression is the factored form of x 3 + 2 x 2 − 5 x − 6 ? x cubed , plus 2 , x squared , minus 5 x minus 6 question mark
    6. ( x + 1 ) ( x + 1 ) ( x − 6 ) open x plus 1 close open x plus 1 close open x minus 6 close
    7. ( x + 3 ) ( x + 1 ) ( x − 2 ) open x plus 3 close open x plus 1 close open x minus 2 close
    8. ( x + 2 ) ( 2 x − 5 ) ( x − 6 ) open x plus 2 close open 2 x minus 5 close open x minus 6 close
    9. ( x − 3 ) ( x − 1 ) ( x + 2 ) open x minus 3 close open x minus 1 close open x plus 2 close

59. A ball with a 3 in. radius has volume V 1 . v sub 1 , .  A second ball has a 9 in. radius and volume V 2 . v sub 2 , .  Which equation represents the volume of the second ball in terms of the first?

    1. V 2 = 3 V 1 v sub 2 , equals 3 , v sub 1
    2. V 2 = 27 V 1 v sub 2 , equals 27 , v sub 1
    3. V 2 = V 1 2 v sub 2 , equals , v sub 1 and super 2
    4. V 2 = 9 V 1 2 v sub 2 , equals 9 , v sub 1 and super 2
60. Extended Response What is the polynomial function, in factored form, whose zeros are − 2 , negative 2 comma  5, and 6, and whose leading coefficient is − 2 ? negative 2 question mark  Graph this function and find any relative minimums or maximums.

Mixed Review

See Lesson 5-1.

Write each polynomial in standard form. Then classify it by degree and by number of terms.

61. x 2 − 1 − 3 x 5 + 2 x 2 x squared , minus 1 minus , 3 x to the fifth , plus , 2 x squared
62. − 2 x 3 − 7 x 4 + x 3 negative 2 , x cubed , minus , 7 x to the fourth , plus , x cubed
63. 6 x + x 3 − 6 x − 2 6 x plus , x cubed , minus 6 x minus 2

See Lesson 4-4.

Factor each expression.

64. x 2 + 5 x + 4 x squared , plus 5 x plus 4
65. x 2 − 2 x − 15 x squared , minus 2 x minus 15
66. x 2 − 12 x + 36 x squared , minus 12 x plus 36

Get Ready! To prepare for Lesson 5-3, do Exercises 67-69.

See Lesson 4-7.

Solve each quadratic equation using any method.

67. x 2 + x − 6 = 0 x squared , plus x minus 6 equals 0
68. 2 x 2 − 7 x + 3 = 0 2 x squared , minus 7 x plus 3 equals 0
69. 4 x 2 − 25 = 0 4 x squared , minus 25 equals 0

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