Graph each function to find the zeros. Rewrite the function with the polynomial in factored form.

54. y = 2 x 2 + 3 x − 5 y equals , 2 x squared , plus 3 x minus 5
55. y = x 4 − 10 x 2 + 9 y equals , x to the fourth , minus , 10 x squared , plus 9
56. y = x 3 − 3 x 2 + 4 y equals , x cubed , minus , 3 x squared , plus 4
57. Open-Ended To solve a polynomial equation, you can use any combination of graphing, factoring, and the Quadratic Formula. Write and solve an equation to illustrate each method.

C Challenge

58. The geometric figure below has volume a 3 + b 3 . eh cubed , plus , b cubed , .  You can split it into three rectangular blocks (including the long one with side a + b eh plus b ). Explain how to use this figure to prove the factoring formula for the sum of cubes, a 3 + b 3 = ( a + b ) ( a 2 − a b + b 2 ) . eh cubed , plus , b cubed , equals open eh plus b close open , eh squared , minus eh b plus , b squared , close .

    
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59. Open-Ended Find equations for two different polynomial functions whose zeros include − 2 , 0 , 1 4 , negative 2 comma 0 comma , 1 fourth , comma  and 1 6 . 1 sixth , .
60. What are the complex solutions of x 5 + x 3 + 2 x = 2 x 4 + x 2 + 1 ? x to the fifth , plus , x cubed , plus 2 x equals , 2 x to the fourth , plus , x squared , plus 1 question mark

Standardized Test Prep

SAT/ACT

61. Which value is NOT a solution to the equation x 4 − 3 x 2 − 54 = 0 ? x to the fourth , minus , 3 x squared , minus 54 equals 0 question mark
    1. − 3 negative 3
    2. 3
    3. − 3 i negative 3 i
    4. − i 6 negative i square root of 6

62. Ava drove 3 hours at 45 miles per hour. How many miles did she drive?

    6. 45 miles
    7. 48 miles
    8. 90 miles
    9. 135 miles
63. Which polynomial has the complex roots 1 + i 2 1 plus i square root of 2  and 1 − i 2 ? 1 minus i square root of 2 question mark
    1. x 2 + 2 x + 3 x squared , plus 2 x plus 3
    2. x 2 − 2 x + 3 x squared , minus 2 x plus 3
    3. x 2 + 2 x − 3 x squared , plus 2 x minus 3
    4. x 2 − 2 x − 3 x squared , minus 2 x minus 3

Short Response

64. Sam has only quarters and dimes in his pocket. He has a total of 12 coins, totaling $1.95. How many of each coin does Sam have?

Mixed Review

See Lesson 5-2.

Write each polynomial in factored form. Check by multiplication.

65. 3 x 2 − 18 x + 24 3 x squared , minus 18 x plus 24
66. 2 x 4 + 6 x 3 − 18 x 2 − 54 x 2 x to the fourth , plus 6 , x cubed , minus , 18 x squared , minus 54 x
67. x 4 − 4 x 3 − 5 x 2 x to the fourth , minus , 4 x cubed , minus , 5 x squared

See Lesson 4-5.

Solve each equation by factoring. Check your answers.

68. x 2 − 4 x = 12 x squared , minus 4 x equals 12
69. x 2 + 1 = 37 x squared , plus 1 equals 37
70. 2 x 2 − 5 x − 3 = 0 2 x squared , minus 5 x minus 3 equals 0

Get Ready! To prepare for Lesson 5-4, do Exercises 71 and 72.

See Lesson 1-3.

Evaluate each expression for the given values of the variables.

71. 16 ( x − 4 ) ( y − 2 ) 4 ( x − 3 ) y ; x = 1 fraction 16 . open , x minus 4 , close . open , y minus 2 , close , over 4 . open , x minus 3 , close . y end fraction . semicolon x equals 1  and y = − 2 y equals negative 2
72. 2 ( x + 5 ) y 10 ( x − 4 ) ( y − 2 ) ; x = 1 fraction 2 . open , x plus 5 , close . y , over 10 . open , x minus 4 , close . open , y minus 2 , close end fraction . semicolon x equals 1  and y = − 2 y equals negative 2

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