AoPS Wiki talk:Problem of the Day/July 1, 2011
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Problem
AoPSWiki:Problem of the Day/July 1, 2011
Solution 1
To factor , we should try to find a way to create a quadratic in disguise. There, in fact, is a way!
Expand and
separately:
We notice that there is a in both of these terms! Treat
as a single quantity,
.
Our original quantity was .
We can factor the original polynomial as .
can be factored as
.
Our final factorization is .
Solution 2
Let . Then
and
(since
). Therefore I have:
where
is a quadratic. Simplifying yields
as before, which is irreducible as
.