document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=822853>Question 822853</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When x^4-8x^2-9 is factored as completely as possible, which of the following is a prime factor ?\r<BR>\n" );
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document.write( "a) (x+1)<BR>\n" );
document.write( "b) (x^2-9)<BR>\n" );
document.write( "c) (x+1)^2<BR>\n" );
document.write( "d) (x+3)<BR>\n" );
document.write( "e) (x^2+9)\r<BR>\n" );
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document.write( "I don't understand it and can someone explain how to go about doing this problem?<BR>\n" );
document.write( "Thanks, much is appreciated.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #495116 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=495116\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The goal is to factor. So we must find two numbers that multiply to -9 (last term) AND add to -8 (middle coefficient). These two numbers are +1 and -9, so we break up the middle term -8x^2 into +1x^2 - 9x^2 and we factor by grouping like so...\r<BR>\n" );
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document.write( "x^4-8x^2-9\r<BR>\n" );
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document.write( "x^4+x^2-9x^2-9\r<BR>\n" );
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document.write( "(x^4+x^2)+(-9x^2-9)\r<BR>\n" );
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document.write( "x^2(x^2+1)+(-9x^2-9)\r<BR>\n" );
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document.write( "x^2(x^2+1)-9(x^2+1)\r<BR>\n" );
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document.write( "(x^2-9)(x^2+1)\r<BR>\n" );
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document.write( "(x^2-3^2)(x^2+1)\r<BR>\n" );
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document.write( "(x-3)(x+3)(x^2+1) ... use the difference of squares rule here\r<BR>\n" );
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document.write( "x^4-8x^2-9\r<BR>\n" );
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document.write( "completely factors to\r<BR>\n" );
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document.write( "(x-3)(x+3)(x^2+1)\r<BR>\n" );
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document.write( "So the final answer (that they want) is <font color=\"red\">d) (x+3)</font><BR>\n" );
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