Name
Class
Date
Chapter 5 Test
Form G
Do you know HOW?
Write each polynomial in standard form. Then classify it by degree and by
number of terms.
1. 4x44 1 6x33 2 2 2 x4
3x 1 6x 2 2;
quartic trinomial
2. 9x2 2
2x 1 3x2
12x2 2 2x; quadratic
binomial
3. 4x(x 2 5)(x 1 6)
4x3 1 4x2 2 120x; cubic
trinomial
4. x4 1 2x2 2 1 5 0
20.64, 0.64
5. 2x3 2 3x 2 2 5 0
20.60
6. 2x4 1 4x3 1 3 5 0
20.85, 4.05
7. 2x3 1 3x 1 4 5 0
2.20
8. x4 1 2x 2 3 5 0
21.57, 1
9. 2x3 1 2x2 1 1 5 0
2.21
Find the real solutions of each equation by graphing. Where necessary, round
to the nearest hundredth.
Write a polynomial function with rational coefficients so that P(x) 5 0 has the
given roots.
10. 2, 3, 5
y 5 x3 2 10x2 1 31x 2 30
11. 21, 21, 1
y 5 x3 1 x2 2 x 2 1
12. !3, 2i
y 5 x4 1 x2 2 12
13. 22i, !5
y 5 x4 2 4x3 1 20x 2 25
Find the zeros of each function. State the multiplicity of any multiple zeros.
14. y 5 (x 2 1)2(2x 2 3)3
1, multiplicity 2; 32 ,
multiplicity 3
15. y 5 (3x 2 2)5(x 1 4)2
24, multiplicity 2; 23 ,
multiplicity 5
Solve each equation.
16. y 5 4x2(x 1 2)3(x 1 1)
21, multiplicity 1;
22, multiplicity 3;
0, multiplicity 2
17. (x 2 1)(x2 1 5x 1 6) 5 0
23, 22, 1
18. x3 2 10x2 1 16x 5 0
0, 2, 8
19. (x 1 2)(x2 1 3x 2 40) 5 0
28, 22, 5
20. x3 1 3x2 2 54x 5 0
29, 0, 6
Divide using synthetic division.
21. (x3 2 4x2 1 x 2 5) 4 (x 1 2)
x2 2 6x 1 13, R 2 31
22. (2x3 2 4x 1 3) 4 (x 2 1)
2x2 1 2x 2 2, R 1
23. (x3 1 5x2 2 x 1 1) 4 (x 1 2)
x2 1 3x 2 7, R 15
24. (3x3 2 x2 1 2x 2 5) 4 (x 2 1)
3x2 1 2x 1 4, R 2 1
Use the Rational Root Theorem to list all possible rational roots for each
equation. Then find any actual roots.
25. x3 1 2x2 1 3x 1 6 5 0
w1, w2, w3, w6; 22
26. x4 2 7x2 1 12 5 0
w1, w2, w3, w4, w6, w12; 22, 2
27. What is P(25) if P(x) 5 2x3 2 4x2 1 x 2 2? 18
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Name
Class
Chapter 5 Test
Date
Form G
(continued)
Expand each binomial.
28. (x 1 y)4
x4 1 4x3y 1 6x2y2 1 4xy3 1 y4
29. (4 2 3x)3
64 2 144x 1 108x2 2 27x3
30. (2r 1 q)5
31. (a 1 4b)3
a3 1 12a2b 1 48ab2 1 64b3
32r5 1 80r4q 1 80r3q2 1 40r2q3 1 10rq4 1 q5
32.
Estimated Number of Deaths in the United States
Year
1960
1970
1980
1990
2000
2003
Deaths
(millions)
1.71
1.92
1.99
2.15
2.40
2.42
SOURCE: www.infoplease.com
a. Find a cubic function to model the data. (Let x 5 years after 1960.) y 5 0.00001065x3 2
b. Estimate the deaths for the year 2006.
0.000584x2 1 0.02241x 1 1.71758
2.55 million
Determine the cubic function that is obtained from the parent function y 5 x3
after each sequence of transformations.
33. a vertical stretch by a factor of 5, a reflection across the y-axis, and a horizontal
translation 2 units left
y 5 5(2x 2 2)3
34. a reflection across the x-axis, a horizontal translation 3 units right, and a
vertical translation 7 units down
y 5 2(x 2 3)3 2 7
Do you UNDERSTAND?
35. Reasoning Would it be a good idea to use the cubic model found in
Exercise 32 to estimate the deaths for the year 2050? Why or why not?
No; answers may vary. Sample: 2050 is far down the cubic model and you have
no way of knowing what might affect the death rate in that many years.
36. Writing How do you use Pascal’s Triangle when expanding a binomial? Pascal’s
Triangle gives you the coefficients of each term in the expanded binomial. You use the
row in the triangle that has its second term the same as the binomial’s exponent.
37. Can a function with the complex roots 5, "2 , and 3i be a fourth-degree No; if a polynomial
polynomial with rational coefficients? Explain. with complex roots 5, !2, and 3i has rational
coefficients, then the complex factors of the polynomial must include (x 2 5), (x 2 !2), (x 1 3i), and
(x 1 3i) , so the polynomial must at least be a fifth-degree polynomial.
38. A cubic box is 5 in. on each side. If each dimension is increased by x in., what
is the polynomial function modeling the new volume V ?
V 5 x3 1 15x2 1 75x 1 125 in.3
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