Exam
Name___________________________________
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the
question.
Determine the coefficient of each term, the degree of each term, and the degree of the polynomial.
1)
–15x4y3– 3x3y +3
8xy
1)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the
question.
Use a vertical format to find the product.
2)
4x3–5x2+6x –8
4x –2
A)
8x4– 30x3+ 36x2– 48x
B)
8x4– 10x3+ 12x2– 16x
C)
16x4–28x3+34x2–44x+16
D)
16x4– 12x3+ 34x2– 20x–16
Use the zero–exponent rule to simplify the expression.
3)
–100
A)
–10
B)
–1
C)
1
D)
0
Simplify the expression using the quotients–to–powers rule.
4)
3p4v3
s2
3
A)
27p12v9
s6
B)
3p12v9
s5
C)
3p12v9
s6
D)
27p7v6
s5
Write the number in decimal notation without the use of exponents.
5)
3.882 x 10–6
A)
–3,882,000
B)
0.0000003882
C)
0.00003882
D)
0.000003882
Solve.
6)
The square garden in the figure measures x yards on each side. The garden is to be expanded so
that one side (the top of the figure) is increased by 3 yards and the adjacent side (the right side of
the figure) is increased by 1yard. Write a polynomial in descending powers of x that expresses
the area of the larger garden. Then use the polynomial to determine the area of the larger garden
if the original garden measures 8 yards on a side.
3 yards
1yard
A)
x2+4x +3; 68 square yards
B)
x2+4; 99 square yards
C)
x2+4x +3; 99 square yards
D)
x2+4; 68 square yards
Subtract the polynomials.
7)
(7x2+ 3x4– 6 – 2x3) – (–8+ 8x3+ 8x4+ 3x2)
A)
–5x4– 10x3+ 4x2+ 2
B)
–5x4+ 6x3+ 10x2– 14
C)
11x4+ 6x3+ 10x2– 14
D)
11x4+ 6x3+ 10x2+ 2
Simplify the expression using the quotients–to–powers rule.
8)
5y
3
2
A)
5y2
3
B)
25y2
3
C)
25y2
9
D)
25y
9
Perform the indicated operations.
9)
[(3x9+ 2) – (–12x7+9x3 )] – [(7x9– 7x5+9x) + (11x3–9x– 10)]
A)
4x9+ 12x7+ 7x5– 20x3+ 12
B)
4x9+ 12x7– 7x5– 20x3+ 12
C)
–4x9+ 12x7– 7x5– 20x3+ 12
D)
–4x9+ 12x7+ 7x5– 20x3+ 12
Provide an appropriate response.
10)
Write 9.68 ×10–4 in decimal notation.
10)
A)
0.000968
B)
0.0000968
C)
–968,000
D)
0.00968
Evaluate the polynomial for the given values of x and y.
11)
11)
4x + 9y – 3; x = – 8 and y = – 6
A)
–93
B)
–86
C)
–98
D)
–89
Simplify the exponential expression.
12)
(3x2)3(2x)–1
12)
A)
27x5
2
B)
9x5
2
C)
6x5
D)
6x4
Use the zero–exponent rule to simplify the expression.
13)
140
13)
A)
–1
B)
0
C)
14
D)
1
Multiply the expression using the product rule.
14)
x7·x7·x8
14)
A)
x15
B)
x22
C)
x57
D)
x14
Evaluate the polynomial for the given values of x and y.
15)
x3+ 3x2y + 3xy2+y3; x = – 2 and y = – 3
15)
A)
–15
B)
25
C)
–35
D)
–125
Perform the indicated computations. Write the answer in scientific notation.
16)
(3 ×10–7)(3 ×106)
16)
A)
90 ×10–1
B)
9×10–42
C)
9×10–1
D)
9×100
Perform the indicated operations.
17)
17)
(5a – 2b)(2a + 4b)
A)
10a2+ 20ab – 8b2
B)
10a2– 4ab – 8b2
C)
10a2+ 16ab + 16b2
D)
10a2+ 16ab – 8b2
Perform the indicated computations. Write the answer in scientific notation.
18)
(4 ×10–5)2
18)
A)
1.6 ×10–2
B)
8×10–10
C)
1.6 ×10–9
D)
8×10–3
Find the product.
19)
19)
(2x – 10)(x + 9)
A)
x2+ 8x + 7
B)
2x2+ 8x – 90
C)
2x2+ 7x – 90
D)
x2– 90x + 8
Multiply by using the rule for the square of a binomial.
20)
(4 – 9x)2
20)
A)
81x2– 16
B)
9x2– 72x + 16
C)
9x2– 16
D)
81x2– 72x + 16
Evaluate the polynomial for the given values of x and y.
21)
2y2–4xy; x = – 7 and y =1
21)
A)
37
B)
127
C)
30
D)
126
Find the product.
22)
(x2– 3x + 1)(5x)
22)
A)
5x3– 15x2– 8x
B)
5x3+16x2+5x
C)
5x3– 15x2+5x
D)
5x3– 14x2+2x
6
Divide using the quotient rule.
23)
x11
x8
23)
A)
x3
B)
x9
C)
1
x3
D)
x19
Graph the equation. Find seven solutions in your table of values for the equation by using integers for x, starting with
–3 and ending with 3.
24)
y =x2–3
x x2–3
–3
–2
–1
0
1
2
3
24)
A)
B)
7
C)
D)
Find the product.
25)
(9x – 1)(x2– 5x + 1)
25)
A)
9x3+46x2– 14x + 1
B)
9x3– 44x2+4x – 1
C)
9x3– 46x2+14x – 1
D)
9x3– 45x2+9x + 1
Use a vertical format to find the product.
26)
6x2+7x +8
x +5
26)
A)
36x3+30x2+35x +13
B)
36x3+42x2+48x
C)
6x3+30x2+35x +40
D)
6x3+37x2+43x +40
8
Subtract the polynomials.
27)
(18y4– 15y3) – (–8y4– 19y3)
27)
A)
30y7
B)
26y4– 34y3
C)
10y4– 34y3
D)
26y4+ 4y3
Multiply the monomials.
28)
(4x5)(–9x4)
28)
A)
–36x20
B)
–36x9
C)
36x9
D)
36x20
Write the number in decimal notation without the use of exponents.
29)
8.843 x 106
29)
A)
884,300
B)
8,843,000
C)
88,430,000
D)
530.58
Multiply using the rule for finding the product of the sum and difference of two terms.
30)
30)
(x + 1)(x – 1)
A)
x2– 1
B)
x2– 2
C)
x2+ 2x – 1
D)
x2– 2x – 1
Write the number in decimal notation without the use of exponents.
31)
5.56 x 10–4
31)
A)
0.00556
B)
0.000556
C)
0.0000556
D)
–556,000
Identify the polynomial as a monomial, binomial, or trinomial. Give the degree of the polynomial.
32)
5x4+
3x3– 7x2
32)
A)
Trinomial, degree 9
B)
Binomial, degree 3
C)
Trinomial, degree 4
D)
Binomial, degree 9
Divide the polynomial by the monomial.
33)
21y6–35y5
7y
33)
A)
3y6– 5y5
B)
3y5– 5y4
C)
3y7– 5y6
D)
21y5–35y4
Add or subtract as indicated.
34)
(6x2– xy –y2) + (x2+10xy +9y2)
34)
A)
6x2+10xy +9y2
B)
7x2+11xy +10y2
C)
5x2– 11xy – 10y2
D)
7x2+9xy +8y2
Write the expression with positive exponents only. Then simplify, if possible.
35)
1
4
–3
35)
A)
64
B)
1
12
C)
–64
D)
1
64
Identify the polynomial as a monomial, binomial, or trinomial. Give the degree of the polynomial.
36)
17x6+ 7x – 1
36)
A)
Trinomial, degree 8
B)
Binomial, degree 7
C)
Trinomial, degree 6
D)
Trinomial, degree 7
Perform the indicated operations.
37)
(3x2y3– xy –y2) + (x2y3+4xy +4y2)
37)
A)
3x2y3+4xy +4y2
B)
4x2y3+5xy +5y2
C)
4x2y3+3xy +3y2
D)
2x2y3– 5xy – 5y2
Identify the polynomial as a monomial, binomial, or trinomial. Give the degree of the polynomial.
38)
38)
8
A)
Binomial, degree 0
B)
Monomial, degree 8
C)
Monomial, degree 1
D)
Monomial, degree 0
Subtract the polynomials.
39)
(8x6– 8x4+ 12) – (4x6+ 13x4– 8)
39)
A)
3x10
B)
4x6– 4x4+ 4
C)
4x6– 21x4+ 20
D)
4x6– 21x4+ 4
11
Perform the indicated computation. Write the answer in scientific notation.
40)
(5.9 ×10–10)(2×10–11)
40)
A)
11.8 ×10–21
B)
1.18 ×10–20
C)
1.18 ×10–21
D)
1.18 ×10–22
Solve.
41)
Approximately 9×103 employees of a certain company average $30,000 each year in salary.
What is the total amount earned by all the employees of this company per year? Write your
answer in scientific notation.
41)
A)
$27 ×108
B)
$2.7 ×109
C)
$27 ×109
D)
$2.7 ×108
Write the number in decimal notation without the use of exponents.
42)
7.27 x 100
42)
A)
1
B)
7.27
C)
72.7
D)
0
Divide using the quotient rule.
43)
x6y12
x2y5
43)
A)
x3y6
B)
x3y7
C)
x4y7
D)
xy7
Multiply the monomials.
44)
1
8x3–1
3x8
44)
A)
1
24 x24
B)
–1
24 x24
C)
1
24 x11
D)
–1
24 x11
Simplify the exponential expression.
45)
y3
y
–2
45)
A)
1
y8
B)
y4
C)
1
y4
D)
1
y7
Graph the equation. Find seven solutions in your table of values for the equation by using integers for x, starting with
–3 and ending with 3.
46)
y =4–x2
x 4–x2
–3
–2
–1
0
1
2
3
46)
13
A)
B)
C)
D)
Multiply the monomials.
47)
–1
5x71
4x9
47)
A)
1
20 x63
B)
1
20 x16
C)
–1
20 x63
D)
–1
20 x16
Add the polynomials.
48)
(7y5+ 8y3) + (6y5– 4y3)
48)
A)
17y8
B)
13y10 + 4y6
C)
17y16
D)
13y5+ 4y3
Divide the polynomial by the monomial.
49)
72x8y9– 72x6y7– 18x2y5
18x2y5
49)
A)
4x6y9– 4x4y7– 1y5
B)
4x8y9– 4x6y7– 1x2y5
C)
–4x6y4– 4x4y2+ 1
D)
4x6y4– 4x4y2– 1
Find the product.
50)
50)
(5x + 6)(5x – 6)
A)
25x2– 36
B)
x2– 36
C)
25x2+ 60x – 36
D)
25x2– 60x – 36
Use a vertical format to find the product.
51)
x3+3x –2
x +12
51)
A)
x4+12x3+3x2+34x –24
B)
x4+3x2–2x +12
C)
x3+15x2+34x –24
D)
x4+12x3+3x2+38x +24
15
Divide the monomials.
52)
–18x8
6x3
52)
A)
x5
B)
x4
C)
–3x5
D)
–3x4
Multiply the monomials.
53)
1
4x81
5x2
53)
A)
–1
20 x16
B)
1
20 x10
C)
1
20 x16
D)
–1
20 x10
Subtract the polynomials.
54)
54)
(4x – 7) – (20x + 19)
A)
–16x – 26
B)
–16x + 12
C)
24x + 12
D)
–42x2
16