document.write( "Question 1116335: factorise completely the following
\n" ); document.write( "a) x^9-y^9
\n" ); document.write( "B)x^4-5x^3+5x^2+5x-6 \n" ); document.write( "

Algebra.Com's Answer #731214 by KMST(5328) $\"\"$ $\"About$

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A) You can use the\"special product $\"%28A-B%29%28A%5E2%2BAB%2BB%5E2%29=A%5E3-B%5E3\"$ twice,
\n" ); document.write( "with $\"system%28A=x%5E3%2CB=y%5E3%29\"$ the first time, and $\"system%28A=x%2CB=y%29\"$ the second time.
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\n" ); document.write( "The last expression is completely factorized.
\n" ); document.write( "A polynomial of the form $\"A%5E2%2BAB%2BB%5E2\"$ is positive as long as $\"AB%3C%3E0\"$ ,
\n" ); document.write( "so it cannot be factored.
\n" ); document.write( "
\n" ); document.write( "B) $\"x%5E4-5x%5E3%2B5x%5E2%2B5x-6\"$
\n" ); document.write( "takes the value $\"0\"$ for $\"x=1\"$ and for $\"x=-1\"$ ,
\n" ); document.write( "so $\"%28x-1%29\"$ and $\"%28x%2B1%29\"$ are factors.
\n" ); document.write( "Dividing by both, you find
\n" ); document.write( " $\"x%5E4-5x%5E3%2B5x%5E2%2B5x-6=highlight%28%28x-1%29%28x%2B1%29%28x%5E2-5x%2B1%29%29\"$
\n" ); document.write( "The last expression is completely factorized,
\n" ); document.write( "unless you wanted to include $\"%28x-%285%2Bsqrt%2821%29%29%2F2%29\"$ and $\"%28x-%285-sqrt%2821%29%29%2F2%29\"$ as factors,
\n" ); document.write( "because the zeros of $\"x%5E2-5x%2B1\"$ are the irrational numbers $\"%285+%2B-+sqrt%2821%29%29%2F2\"$ \n" ); document.write( "

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