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Contests
National and Regional Contests
USA Contests
MAA AMC
AMC 12/AHSME
1986 AMC 12/AHSME
23
23
Part of
1986 AMC 12/AHSME
Problems
(1)
Polynomial factoring
Source: AHSME 1986 problem 23
10/1/2011
Let
N
=
6
9
5
+
5
⋅
6
9
4
+
10
⋅
6
9
3
+
10
⋅
6
9
2
+
5
⋅
69
+
1.
N = 69^{5} + 5\cdot 69^{4} + 10\cdot 69^{3} + 10\cdot 69^{2} + 5\cdot 69 + 1.
N
=
6
9
5
+
5
⋅
6
9
4
+
10
⋅
6
9
3
+
10
⋅
6
9
2
+
5
⋅
69
+
1.
How many positive integers are factors of
N
N
N
?
<
s
p
a
n
c
l
a
s
s
=
′
l
a
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x
−
b
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>
(
A
)
<
/
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a
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>
3
<
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a
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a
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o
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>
(
B
)
<
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5
<
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c
l
a
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a
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x
−
b
o
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′
>
(
C
)
<
/
s
p
a
n
>
69
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
125
<
s
p
a
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c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
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>
216
<span class='latex-bold'>(A)</span>\ 3\qquad<span class='latex-bold'>(B)</span>\ 5\qquad<span class='latex-bold'>(C)</span>\ 69\qquad<span class='latex-bold'>(D)</span>\ 125\qquad<span class='latex-bold'>(E)</span>\ 216
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
3
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
5
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
69
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
125
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
216
algebra
polynomial
AMC