document.write( "Question 137778This question is from textbook Algebra Structure and Method
\n" ); document.write( ": I have been having trouble on this problem for awhile now and I was wondering if anyone could help me? Please and Thank You!! I would deeply appreciate it!\r
\n" ); document.write( "\n" ); document.write( "Factor completely. check for a greatest common factor first.
\n" ); document.write( "X^8-1 \n" ); document.write( "
Algebra.Com's Answer #100744 by Fombitz(32388)\"\" \"About 
You can put this solution on YOUR website!
Problems of the form
\n" ); document.write( "\"z%5E2-b%5E2\" factor in this fashion
\n" ); document.write( "\"z%5E2-b%5E2=%28z-b%29%28z%2Bb%29\"
\n" ); document.write( "We can make a substitution to get it into this form.
\n" ); document.write( "Let
\n" ); document.write( "\"z=x%5E4\"
\n" ); document.write( "\"b=1\"
\n" ); document.write( "Therefore
\n" ); document.write( "\"z%5E2-b%5E2=x%5E8-1=%28x%5E4-1%29%28x%5E4%2B1%29\"
\n" ); document.write( "Similarly
\n" ); document.write( "\"x%5E4-1=%28x%5E2-1%29%28x%5E2%2B1%29\"
\n" ); document.write( "and
\n" ); document.write( "\"x%5E2-1=%28x-1%29%28x%2B1%29\"
\n" ); document.write( "Substituting all of those in, you get
\n" ); document.write( "\"x%5E8-1=%28x-1%29%28x%2B1%29%28x%5E2%2B1%29%28x%5E4%2B1%29\"
\n" ); document.write( "The roots of \"x%5E2%2B1\" are (i, -i).
\n" ); document.write( "\"x%5E8-1=%28x-1%29%28x%2B1%29%28x%2Bi%29%28x-i%29%28x%5E4%2B1%29\"
\n" ); document.write( "Finally if we do a substitution of \"u=x%5E2\" we get,
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\n" ); document.write( "When we put that all together we get,
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\n" ); document.write( "You can check on the square root of i and -i.
\n" ); document.write( "The four roots are of the form
\n" ); document.write( "\"x=0+%2B-+%281%2Fsqrt%282%29%29%281+%2B-+i%29\"
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