document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=540791>Question 540791</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Is this correct and what are the prime numbers 5,1 or 5,3?\r<BR>\n" );
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document.write( "Factor completely. If polynomial is a prime state this.<BR>\n" );
document.write( "15tē+20t-75 factor GCF<BR>\n" );
document.write( "5(3tē+4t-15)<BR>\n" );
document.write( "5(3tē+9t-5t-15)<BR>\n" );
document.write( "5(3t(t+3)-5(t+3)<BR>\n" );
document.write( "5[(3t-5)(9t+3)] get rid of parentheses <BR>\n" );
document.write( "5(3t-5)(t+3) no negative factors so the sign will not change<BR>\n" );
document.write( "GCF=5<BR>\n" );
document.write( "Prime = 5,3<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #353873 by </B><A HREF=/tutors/aboutme.mpl?userid=fcabanski><B>fcabanski(1391)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=fcabanski><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=353873\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Your factoring is correct.<P><BR>\n" );
document.write( "1 is not a prime number.<P><BR>\n" );
document.write( "But the question \"is it prime\" has nothing to do with 5 and 3 or 5 and 1.<P><BR>\n" );
document.write( "You cannot factor a prime polynomial.  You'd have to use the quadratic formula.<P><BR>\n" );
document.write( "The fact that you were able to factor it proves it isn't prime.<P><BR>\n" );
document.write( "The test for prime is step 1.  If it's prime, use the quadratic.<P><BR>\n" );
document.write( "Remember the general quadratic polynomial is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2+%2B+bx+%2B+c ALIGN=MIDDLE  ALT=\"ax%5E2+%2B+bx+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "To test for prime determine if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2+-4ac ALIGN=MIDDLE  ALT=\"b%5E2+-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >, that's called the discriminant, is a perfect square.  If it is, then the polynomial isn't prime and you can factor it.<P><BR>\n" );
document.write( "In this case the discriminant is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%5E2+-+4%2A15%2A75+=+4900+=+70%2A70 ALIGN=MIDDLE  ALT=\"20%5E2+-+4%2A15%2A75+=+4900+=+70%2A70\"   DISABLED_style= \"max-width:90%; height:auto;\" ><P><BR>\n" );
document.write( "4900 is a perfect square, so the polynomial is not prime.<BR>\n" );
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