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Mathematics Its Power and Utility
Quiz 3: Introduction to Algebra
Path 4
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Question 41
Short Answer
Simplify the expression as completely as possible.
(
5
a
)
(
2
a
)
(
6
a
)
( 5 a ) ( 2 a ) ( 6 a )
(
5
a
)
(
2
a
)
(
6
a
)
Question 42
Short Answer
Simplify the expression as completely as possible.
(
ā
3
x
3
)
(
2
x
)
2
\left( - 3 x ^ { 3 } \right) ( 2 x ) ^ { 2 }
(
ā
3
x
3
)
(
2
x
)
2
Question 43
Short Answer
Simplify the expression as completely as possible.
6
a
(
ā
3
b
)
(
ā
a
)
(
ā
3
b
)
6 a ( - 3 b ) ( - a ) ( - 3 b )
6
a
(
ā
3
b
)
(
ā
a
)
(
ā
3
b
)
Question 44
Short Answer
Simplify the expression.
(
ā
3
x
)
(
2
y
)
( - 3 x ) ( 2 y )
(
ā
3
x
)
(
2
y
)
Question 45
Matching
Match each description below with the letter of the corresponding polynomial.
Premises:
Responses:
3
rd
degree trinomial
3
x
4
y
3
3 x ^ { 4 } y ^ { 3 }
3
x
4
y
3
7
th
degree monomial
z
ā
x
ā
y
z - x - y
z
ā
x
ā
y
1
st
degree trinomial
2
z
7
ā
3
2 z ^ { 7 } - 3
2
z
7
ā
3
Premises:
3
rd
degree trinomial
7
th
degree monomial
1
st
degree trinomial
Responses:
3
x
4
y
3
3 x ^ { 4 } y ^ { 3 }
3
x
4
y
3
z
ā
x
ā
y
z - x - y
z
ā
x
ā
y
2
z
7
ā
3
2 z ^ { 7 } - 3
2
z
7
ā
3
Question 46
Short Answer
Find the product.
(
4
c
2
)
(
2
c
4
)
\left( 4 c ^ { 2 } \right) \left( 2 c ^ { 4 } \right)
(
4
c
2
)
(
2
c
4
)
Question 47
Short Answer
Use the definition of exponent and the addition law of exponents to multiply the algebraic expression.
x
3
t
3
x
5
x ^ { 3 } t ^ { 3 } x ^ { 5 }
x
3
t
3
x
5
Question 48
Short Answer
Multiply.
3
x
(
ā
4
y
)
(
ā
x
)
(
ā
4
y
)
3 x ( - 4 y ) ( - x ) ( - 4 y )
3
x
(
ā
4
y
)
(
ā
x
)
(
ā
4
y
)
Question 49
Short Answer
Simplify the expression as completely as possible.
ā
a
a
6
a
2
- a a ^ { 6 } a ^ { 2 }
ā
a
a
6
a
2
Question 50
Short Answer
Use the definition of exponent and the addition law of exponents to multiply the algebraic expression.
x
2
t
5
t
2
x
5
x ^ { 2 } t ^ { 5 } t ^ { 2 } x ^ { 5 }
x
2
t
5
t
2
x
5
Question 51
Short Answer
Give the degree and the numerical coefficient of the following term.
7
x
3
7 x ^ { 3 }
7
x
3
coefficient = __________ degree = __________
Question 52
Short Answer
Simplify the expression as completely as possible.
(
ā
4
w
2
)
(
ā
2
w
4
)
\left( - 4 w ^ { 2 } \right) \left( - 2 w ^ { 4 } \right)
(
ā
4
w
2
)
(
ā
2
w
4
)
Question 53
Short Answer
How many terms are contained in a binomial?
Question 54
Short Answer
Use the definitions of exponent and the addition law of exponents to multiply the algebraic expressions.
4
t
2
(
ā
2
t
2
)
(
ā
4
t
3
)
4 t ^ { 2 } \left( - 2 t ^ { 2 } \right) \left( - 4 t ^ { 3 } \right)
4
t
2
(
ā
2
t
2
)
(
ā
4
t
3
)
Question 55
Matching
Match each polynomial below with the letter of the corresponding polynomial type.
Premises:
Responses:
18
c
2
18 c ^ { 2 }
18
c
2
binomial
14
d
+
c
14 d + c
14
d
+
c
trinomial
10
ā
9
c
8
+
15
d
10 - 9 c ^ { 8 } + 15 d
10
ā
9
c
8
+
15
d
monomial
Premises:
18
c
2
18 c ^ { 2 }
18
c
2
14
d
+
c
14 d + c
14
d
+
c
10
ā
9
c
8
+
15
d
10 - 9 c ^ { 8 } + 15 d
10
ā
9
c
8
+
15
d
Responses:
binomial
trinomial
monomial
Question 56
Short Answer
If m < 3 , then the endpoint is __________ ( an open dot / a closed dot ).
Question 57
Short Answer
A plumber cuts a pipe that is 16 feet long into
x
x
x
equal pieces. Find an expression for the length of each piece.
Question 58
Short Answer
Suppose that 5 times a number is added to 10 and the result is negative. What are the possible solutions? Any number __________ ( greater than / less than / greater than or equal to / less than or equal to) __________.