5
1. x; product of
powers property
10
x
2. }
; power
15
32y
of a product
property,
negative
exponent
property
8 4
3. x y ; power
of a quotient
property,
negative
exponent
property
3x 3y 3
4. }3;
27x 2 5y
power of a
product property
CHAPTER TEST
1014#5-31 odd, 407#choose 6
Simplify the expression. Tell which properties of exponents you used.
1. x 3 p x2 p x24
x24
3. }}
y2
22
Assessment Book
3(xy)3
4. }}}}}3
27x 2 5y
1 2
2. (2x22y 3)25
Chapter Test, Levels A, B, C
Standardized Chapter Test
• SAT/ACT Chapter Test
• Alternative Assessment
•
•
Graph the polynomial function. 5–7. See margin.
5. f(x) 5 2x 3
6. f (x) 5 x 4 2 2x2 2 5x 1 1
7. f (x) 5 x5 2 x4 2 9
Perform the indicated operation.
8. (2x 3 1 5x 2 2 7x 1 4) 1 (x 3 2 3x2 2 4x)
3x 1 2x 2 11x 1 4
3
2
10. (3x 2 2)(x2 1 4x 2 7)
2
14. 8x 3 1 27
3x 2 5x 2 x 1 3
3
15. x4 1 5x 2 2 6
(2x 1 3)(4x 2 2 6x 1 9)
Find all real zeros of the function.
Test Generator
9. (3x 3 2 4x2 1 3x 2 5) 2 (x2 1 4x 2 8)
2
Chapter Test
11. (3x 2
5) 3
2
1 225x 2 125
27x43 2 135x
13. (6x 1 7x 2 1 4x 2 17) 4 (3x2 2 3x 1 2)
9x 2 23
2x 2 1 2x 1 3 1 }
2x 2 2 3x 1 3
3x 1 10x 2 29x 1 14
12. (3x 3 2 14x2 1 16x 2 22) 4 (x 2 4)
10
3x 2 2 2x 1 8 1 }
x24
Factor the polynomial completely.
3
22. x 4 2 10x 3 1
32x 2 2 92x 1 60
(x 2 3)(x 2 2)(x 1 2)
1 1
18. f (x) 5 4x4 2 8x 3 2 19x2 1 23x 2 6 22, }, }, 3
2 2
17. f(x) 5 x 3 1 x 2 2 22x 2 40 24, 22, 5
5.
20. 6, 2i
21. 23, 21, 1 2 Ï 5
22. 1 1 3i, 4 1 Ï 10
x 3 2 6x 2 1 5x 1 12
x 3 2 6x 2 1 4x 2 24
Use a graphing calculator to graph the function. Identify the x-intercepts
and the points where the local maximums and local minimums occur.
19. 21, 3, 4
-0580.indd
2:23:25
PM 407
x
1
2
3
4
f(x)
3
1
1
3
2
21
x
1
2
3
4
5
6
7
13
f(x)
0
27
24
21
80
185
f (x) 5 x 2 5x 1 7
21
x
f (x) 5 2x 2 7x 2 1 5
3
of the United States was about 1.099 3 1013 dollars. The population of the
U.S. in 2003 was about 2.91 3 108. What was the per capita GDP in 2003?
7.
about $37,766
28. TELEVISION From 1980 to 2002, the number T (in millions) of households
in the United States with televisions and the percent P of those households
with VCRs can be modeled by
and
y
1
6
27. GROSS DOMESTIC PRODUCT In 2003, the gross domestic product (GDP)
x
6.
5
2
T 5 1.22x 1 76.9
y
}
}
3
2
24. f (x) 5 x4 1 3x 3 2 x 2 2 6x 1 2
23. x-intercepts: 23. f(x) 5 x 2 5x 1 3x 1 4
20.62, 1.6, 4;
local maximum: Use finite differences and a system of equations to find a polynomial function that
(0.33, 4.5); local fits the data in the table.
minimum: (3, 25) 25.
26.
24. x-intercepts:
0.34, 1.1; local
maximum:
(20.88, 5.1);
local minimums:
(22.2, 1.8), (0.79,
21.5)
Easily-readable reduced copies (with answers) of Chapter
Test B, the Standardized
Chapter Test, and the
Alternative Assessment from
the Assessment Book can be
found on pp. 328G–328H.
16. x 3 2 3x 2 2 4x 1 12
(x 2 1)(x 1 1)(x 2 1 6)
Write a polynomial function f of least degree that has rational coefficients, a
leading coefficient of 1, and the given zeros.
21. x 4 1 2x 3 2
9x 2 2 22x 2 12
Additional Resources
y
2
21
x
P 5 20.205x2 1 8.36x 1 1.98
where x is the number of years since 1980. Write a polynomial model for
the total number of U.S. households with both televisions and VCRs.
y 5 20.2501x 3 2 5.5653x 2 1 645.3x 1 152.262
GEOMETRY A rectangular prism has edges of lengths x, x 1 2, and
29.
2x 2 3 inches. The volume of the prism is 1040 cubic inches. Write a
polynomial equation that models the prism’s volume. What are the prism’s
dimensions? 1040 5 2x 3 1 x 2 2 6x; 8 in. by 10 in. by 13 in.
Chapter Test
407
7/7/09 8:41:41 AM
407