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Math Problems
Grade 6
Prime factorization
Q.
2
2
2
Given the probability distribution:
X
X
X
0
0
0
1
1
1
2
2
2
3
3
3
P
(
x
)
P(x)
P
(
x
)
1
10
\frac{1}{10}
10
1
3
10
\frac{3}{10}
10
3
1
2
\frac{1}{2}
2
1
1
10
\frac{1}{10}
10
1
Let
0
0
0
0
0
0
Find the probability distribution of
0
0
0
1
1
1
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Write all the factors of
20
20
20
. Use commas to separate them.
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The polynomial
\newline
has a known factor of
\newline
.
\newline
Rewrite
\newline
as a product of linear factors.
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7
7
7
. Which expression shows a prime factorization?
\newline
A.
2
⋅
9
⋅
11
2 \cdot 9 \cdot 11
2
⋅
9
⋅
11
\newline
B.
2.5
⋅
7
⋅
3
2.5 \cdot 7 \cdot 3
2.5
⋅
7
⋅
3
\newline
C.
1
⋅
11
⋅
13
1 \cdot 11 \cdot 13
1
⋅
11
⋅
13
\newline
D.
2
⋅
2
⋅
2
⋅
3
⋅
11
2 \cdot 2 \cdot 2 \cdot 3 \cdot 11
2
⋅
2
⋅
2
⋅
3
⋅
11
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If
f
(
x
)
=
2
x
3
+
14
x
2
−
32
x
+
36
f(x)=2 x^{3}+14 x^{2}-32 x+36
f
(
x
)
=
2
x
3
+
14
x
2
−
32
x
+
36
and
x
+
9
x+9
x
+
9
is a factor of
f
(
x
)
f(x)
f
(
x
)
, then find all of the zeros of
f
(
x
)
f(x)
f
(
x
)
algebraically.
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Given that
Z
=
2
2
×
3
2
×
5
2
×
7
p
Z=2^{2} \times 3^{2} \times 5^{2} \times 7^{p}
Z
=
2
2
×
3
2
×
5
2
×
7
p
, express
70
Z
70 Z
70
Z
as a product of powers of its prime factors.
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x
=
0
,
1
,
2
,
3
,
4
x= 0, 1, 2, 3, 4
x
=
0
,
1
,
2
,
3
,
4
and
y
=
26
,
27
,
18
,
9
,
0
y= 26, 27, 18, 9, 0
y
=
26
,
27
,
18
,
9
,
0
which of the following equations relates
y
y
y
to
x
x
x
for the values in the table?
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To find the largest natural number less than
100
100
100
that is equal to the sum of
6
6
6
consecutive natural numbers, we can start by looking at the sum of the first few consecutive natural numbers.
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A piece of paper is to display
150
150
150
square inches of text. If there are to be one-inch margins on the sides and the top and a two-inch margin at the bottom, what are the dimensions of the smallest piece of paper that can be used?
\newline
Choose
1
1
1
answer:
\newline
(A)
6
′
′
25
′
′
6 \prime \prime 25 \prime \prime
6′′25′′
\newline
(B)
10
′
×
15
′
10 \prime \times 15 \prime
10′
×
15′
\newline
(C)
12
′
×
18
′
12 \prime \times 18 \prime
12′
×
18′
\newline
(D)
15
′
′
18
′
15 \prime \prime 18 \prime
15′′18′
\newline
(E) None of these
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Factor
48
−
8
x
48-8x
48
−
8
x
to identify the equivalent expressions.
\newline
Choose
2
2
2
answers:
\newline
A)
3
(
16
−
8
x
)
3(16-8x)
3
(
16
−
8
x
)
\newline
B)
2
(
24
−
4
x
)
2(24-4x)
2
(
24
−
4
x
)
\newline
C)
8
(
6
−
x
)
8(6-x)
8
(
6
−
x
)
\newline
D)
4
(
12
−
2
x
)
4(12-2x)
4
(
12
−
2
x
)
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