Difference between revisions of "2022 AMC 12A Problems/Problem 21"
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By difference of powers, <math>x^9-1=(x^3-1)(x^6+x^3+1)</math>. | By difference of powers, <math>x^9-1=(x^3-1)(x^6+x^3+1)</math>. | ||
Therefore, the answer is E. | Therefore, the answer is E. | ||
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+ | == Video Solution by ThePuzzlr == | ||
+ | |||
+ | https://youtu.be/YRcaIrwA2AU | ||
+ | |||
+ | ~ MathIsChess |
Revision as of 10:47, 12 November 2022
Solution
is equal to
by difference of powers.
Therefore, the answer is a polynomial that divides but not
.
Note that any polynomial divides
if and only if
is a factor of
.
The prime factorizations of and
are
and
, respectively.
Hence, is a divisor of
but not
.
By difference of powers, .
Therefore, the answer is E.
Video Solution by ThePuzzlr
~ MathIsChess