Name _______________________________________ Date __________________ Class __________________
LESSON
7-1
Finding Rational Solutions of Polynomial Equations
Practice and Problem Solving: C
Solve each polynomial equation by factoring.
1. 3 x 4  6 x 3  105 x 2  0
2. 8 x 7  56x 6  96x 5  0
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Identify the rational zeros of each function. Then write the function in
factored form.
3. f ( x )  x 3  6x 2  12x  8
4. f ( x )  x 3  10x 2  32x  32
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Identify all the rational roots of each equation.
5. x 3  2x 2  48x  0
6. 5 x 4  19 x 3  29 x 2  5 x  0
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7. 6x 3  12x 2  18x  0
8. 3x 4  5x 3  11x 2  3x  0
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Solve.
9. A jewelry box is designed such that its length is twice its width and its
depth is 2 inches less than its width. The volume of the box is 64 cubic
inches.
a. Write an equation to model the volume of the box.
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b. List all possible rational roots. ________________________________________________________
c. Use synthetic division to find the roots of the polynomial equation. Are the roots all
rational numbers?
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d. What are the dimensions of the box? _________________________________________________
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Name _______________________________________ Date __________________ Class __________________
LESSON
7-2
Finding Complex Solutions of Polynomial Equations
Practice and Problem Solving: C
Write the simplest polynomial function with the given roots.
3
1.  , 6, and  1
4
2. 5i , 2, and 7
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_________________________________
3. i ,  3, and  1
4. 2i , 4, and 6
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Solve each equation by finding all roots.
5. 4x 4  8x 3  3x 2  18x  27  0
6. x 4  3x 3  x 2  9x  12  0
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7. x 4  3x 3  8x 2  22x  24  0
8. x 3  6x 2  4x  24  0
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Solve.
9. For a scientific experiment, Tony needs a glass bell jar in the shape of
a cylinder with a hemisphere on top. The height of the cylinder must be
3 inches longer than its radius, and the volume must be 72 cubic
inches. What should the radius of the cylinder be?
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Name _______________________________________ Date __________________ Class __________________
ANSWERS
7-1 Practice and Problem Solving C
1. x  5, x  0, or x  7
2. x  0, x  3, or x  4
3. x  2; f  x    x  2
3
4. x  4, x  2; f  x    x  2 x  4
2
5. x  8, x  0, or x  6
1
, or x  1
5
7. x  3, x  0, or x  1
6. x  5, x  0, x 
8. x  3, x  0, x 
1
, or x  1
3
9. a. 2x 3  4 x 2  64  0
b. 1,  2,  4,  8,  16,  32,  64
c. x  4, or x  1  i 7; no, 2 of the
roots are irrational numbers
d. 4 in. wide, 8 in. long, and 2 in. deep
7-2 Practice and Problem Solving C
1. P ( x )  x 3 
17 2 39
9
x 
x
4
4
2
2. P(x)  x4  9x3  39x2  225x  350
3. P(x)  x4  4x3  4x2  4x  3
4. P(x)  x5  4x4  2x3  8x2  24x  96
5. x  
3 3
i , i , 3, and  1
2 2
6. x  i 3,  i 3, 1, and  4
7. x  1  i, 1  i, 3, and 4
8. x  2i, 2i, and 6
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