5-5 Solving Polynomial Equations
Solve each equation.
Solve each equation.
4
2
61. 18x + 43x – 5 = 0
3
35. 64x + 1 = 0
SOLUTION: SOLUTION: 2
Let u = x .
Therefore, the solutions are
.
Write each expression in quadratic form, if
possible.
10
5
41. 16x + 2x + 6
SOLUTION: 5
Let y = 2x .
The solutions are
4
.
2
63. 3x – 22x – 45 = 0
SOLUTION: 2
Let u = x .
Solve each equation.
4
2
61. 18x + 43x – 5 = 0
SOLUTION: 2
Let u = x .
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The solutions are
.
The solutions
are
.
5-5 Solving
Polynomial
Equations
4
2
The solutions are
6
3
63. 3x – 22x – 45 = 0
65. x – 26x – 27 = 0
SOLUTION: SOLUTION: 2
.
3
Let u = x .
Let u = x .
Solve each equation for x.
The solutions are
6
.
3
65. x – 26x – 27 = 0
SOLUTION: 3
Let u = x .
Solve each equation for x.
The solutions are –1, 3,
4
2
, and
.
2
67. 4x – 4x – x + 1 = 0
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Page 2
2
Let u = x .
5-5 Solving
Polynomial
The solutions
are –1, Equations
3,
4
2
, and
.
2
The solutions are
.
70. CCSS SENSE-MAKING A rectangular prism with
dimensions x – 2, x – 4, and x – 6 has a volume equal
to 40x cubic units.
a. Write out a polynomial equation using the formula
for volume.
b. Use factoring to solve for x.
c. Are any values for x unreasonable? Explain.
d. What are the dimensions of the prism?
67. 4x – 4x – x + 1 = 0
SOLUTION: 2
Let u = x .
SOLUTION: a. The volume of the prism is
.
By Zero Product Property:
Therefore,
b. Solve for x.
By Zero Product Property:
The solutions are
4
.
2
69. x + 8x + 15 = 0
SOLUTION: The solutions are
and 12.
c. Sample answer: ±2i because they are imaginary
numbers.
2
Let u = x .
d. x – 2 =12 – 2 = 10
x – 4 = 12 – 4 = 8
x – 6 = 12 – 6 = 6
By Zero Product Property:
The dimensions are 6, 8 and 10 units.
73. HOME BUILDING Alicia’s parents want their
basement home theater designed according to the
diagram.
The solutions are
.
70. CCSS SENSE-MAKING A rectangular prism with
dimensions x – 2, x – 4, and x – 6 has a volume equal
to 40x cubic units.
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a. Write out a polynomial equation using the formula
for volume.
b.
Page 3
The dimensions are 6, 8 and 10 units.
HOMEPolynomial
BUILDINGEquations
Alicia’s parents want their
73. Solving
5-5
basement home theater designed according to the
diagram.
Therefore, x = 11 or –15.25.
–15.25 is irrelevant because length cannot be
negative. Therefore, x = 11 ft.
74. BIOLOGY A population of parasites in an
3
a. Write a function in terms of x for the area of the
basement.
b. If the basement is to be 1366 square feet, what is
x?
2
experiment can be modeled by f (t) = t + 5t – 4t –
20, where t is the time in days.
a. Use factoring by grouping to determine the values
of t for which f (t) = 0.
b. At what times does the population reach zero?
c. Are any of the values of t unreasonable? Explain.
SOLUTION: a. Substitute 0 for x and solve for x.
SOLUTION: a.
Therefore, the values of t are 2, –2 and –5.
b. The population reaches zero in 2, –2 and –5 days.
c. –2 and –5 are unreasonable because time cannot
be negative.
Factor completely. If the polynomial is not
factorable, write prime.
6
4
4
2
2
75. x – 4x – 8x + 32x + 16x – 64
The area of the basement in terms of x is
.
SOLUTION: 2
Let y = x .
2
Therefore, f (x) = 8x + 34x + 24.
b. Substitute 1366 for f (x) and solve for x.
80. CHALLENGE Solve
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Therefore, x = 11 or –15.25.
–15.25 is irrelevant because length cannot be
negative. Therefore, x = 11 ft.
SOLUTION: Page 4
5-5 Solving Polynomial Equations
80. CHALLENGE Solve
SOLUTION: Let
.
By Zero Product Property:
The solutions are
.
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