document.write( "Question 635918: how do you factor x to the sixth power plus one \n" ); document.write( "

Algebra.Com's Answer #400642 by KMST(5396) $\"\"$ $\"About$

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To factor $\"x%5E6%2B1\"$ , I would think of
\n" ); document.write( " $\"y%5E3%2B1=%28y%2B1%29%28y%5E2-y%2B1%29\"$ , which is a full factorization,
\n" ); document.write( "because if $\"y%5E2-y%2B1\"$ had factors (with real coefficients),
\n" ); document.write( " $\"y%5E2-y%2B1=0\"$ would have real solutions (and it does not).
\n" ); document.write( "If we make $\"y=x%5E2\"$ in $\"y%5E3%2B1=%28y%2B1%29%28y%5E2-y%2B1%29\"$ , we get
\n" ); document.write( " $\"highlight%28x%5E6%2B1=%28x%5E2%2B1%29%28x%5E4-x%5E2%2B1%29%29\"$ \n" ); document.write( "

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