document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1208350>Question 1208350</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Show that x^2 + 9 is prime.\r<BR>\n" );
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document.write( "I will first list the pairs of integers whose product is 9.\r<BR>\n" );
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document.write( "1, 9\r<BR>\n" );
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document.write( "-1, -9\r<BR>\n" );
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document.write( "3, 3\r<BR>\n" );
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document.write( "-3, -3\r<BR>\n" );
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document.write( "2. Compute their sums.\r<BR>\n" );
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document.write( "1 + 9 = 10\r<BR>\n" );
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document.write( "-1 + (-9) = -10\r<BR>\n" );
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document.write( "3 + 3 = 6\r<BR>\n" );
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document.write( "-3 + (-3) = -6\r<BR>\n" );
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document.write( "I can also say x^2 + 9 = x^2 + 0x + 9 and none of the sums added above equal 0. This leads me to conclude that x^2 + 9 is prime.\r<BR>\n" );
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document.write( "1. Do you agree?\r<BR>\n" );
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document.write( "2. How is this done for a trinomial?\r<BR>\n" );
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document.write( "Sample:\r<BR>\n" );
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document.write( "Show that x^1 + x + 1 is prime. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #846727 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=846727\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "You clearly have not stated the problem correctly; or else the problem is faulty.<br><BR>\n" );
document.write( "If x is any multiple of 3, then x^2+9 is not prime.<br><BR>\n" );
document.write( "If x is any odd integer, then x^2 is odd, so x^2+9 is even, so it is not prime.<br><BR>\n" );
document.write( "-------------------------------------------------------<br><BR>\n" );
document.write( "To the student, who suggests in his \"thank you\" note that I didn't know what to do with his question....<br><BR>\n" );
document.write( "It is YOU who does not know what to do.  You posted a problem without the required context.<br><BR>\n" );
document.write( "Without any context, when you ask \"is x^2+9 prime\", the usual interpretation is that you are talking about prime numbers.<br><BR>\n" );
document.write( "If you had posted your problem to ask whether \"x^2+9 is a prime polynomial\", then you would have saved both of us some wasted time.<br><BR>\n" );
document.write( " </SPAN>\n" );
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