document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=725215>Question 725215</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, <BR>\n" );
document.write( "May I ask for help with the following questions?\r<BR>\n" );
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document.write( "Factor the trinomials-<BR>\n" );
document.write( "6x^2+31x+5<BR>\n" );
document.write( "I think that this cannot be factored. \r<BR>\n" );
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document.write( "Also,<BR>\n" );
document.write( "X^2-8xy+12y^2\r<BR>\n" );
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document.write( "I can't seem to move on from these two questions. Thank you for your help.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #444024 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=444024\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Of course it can be factored.  Here is how to tell quickly.  Square the coefficient on the first degree term:  31 times 31 is 961.  Multiply 4 times the lead coefficient times the constant term.  4 times 6 times 5 is 120.  Subtract the second result from the first:  961 minus 120 is 841.  Then take the square root of that result.  If it is a perfect square, and in this case square root of 841 is exactly 29, then the quadratic trinomial is factorable over the rational numbers.\r<BR>\n" );
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document.write( "Here is a process that you might try.  Multiply the lead coefficient times the constant term.  List the two number factorizations of this product.  Find a pair of factors that when summed equal the first degree term coefficient.  6 times 5 is 30.  30 times 1 is 30, and 30 plus 1 is 31 which is your middle term coefficient.  Re-write your trinomial into a four term polynomial splitting the middle term as suggested by the above factorization:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 6x^2\ +\ 30x\ +\ x\ +\ 5\">\r<BR>\n" );
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document.write( "Then group the two pairs of factors:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(6x^2\ +\ 30x\right)\ +\ \left(x\ +\ 5\right)\">\r<BR>\n" );
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document.write( "Factor the GCF out of each group:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 6x\left(x\ +\ 5)\ +\ 1\left(x\ +\ 5\right)\">\r<BR>\n" );
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document.write( "Properly performed, the two binomial factors should be identical for a factorable quadratic, so factor out the binomials:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(6x\ +\ 1\right)\left(x\ +\ 5\right)\ =\ 6x^2\ +\ 31x\ +\ 5\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "<font face=\"Math1\" size=\"+2\">Egw to Beta kai to Sigma</font><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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