document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=173398>Question 173398</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Factor the quadratic equation.<BR>\n" );
document.write( "3x^2+13x-10<BR>\n" );
document.write( "From what I know, one has to find the factors of -10, which are 2 and 5, and 10 and 1, including the negatives. After that, I think one has to find the sums that equal 13x, but I don't see how that would be possible. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #128247 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=128247\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You have only considered half of the problem.  What you said is true IF the coefficient on the high order term is 1, but here it is 3.\r<BR>\n" );
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document.write( "The part about needing the factors of 10 is almost right.  In fact you need the factors of -10.  So, -2 and 5, 2 and -5, -1 and 10, or 1 and -10.\r<BR>\n" );
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document.write( "But the sum required to get the 13 coefficient must consider the 3 coefficient on the high order term.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2+%2B+15+=+13 ALIGN=MIDDLE  ALT=\"-2+%2B+15+=+13\"   DISABLED_style= \"max-width:90%; height:auto;\" >, but <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15=3%2A5 ALIGN=MIDDLE  ALT=\"15=3%2A5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B5%29%283x-2%29=3x%5E2-2x%2B15x-10=3x%5E2%2B13x-10 ALIGN=MIDDLE  ALT=\"%28x%2B5%29%283x-2%29=3x%5E2-2x%2B15x-10=3x%5E2%2B13x-10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Yeah, but how do I know that a quadratic trinomial is factorable in the first place so I don't go rooting (so to speak) around for factors that might not exist? you ask.\r<BR>\n" );
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document.write( "Use the discriminant part of the quadratic formula, <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;\" > where a, b, and c are the coefficients of the 2nd degree, 1st degree, and constant terms respectively.  If the number is a perfect square, then the quadratic is factorable, otherwise not.  For the given problem, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%5E2-4%283%29%28-10%29=169%2B120=289=17%5E2 ALIGN=MIDDLE  ALT=\"13%5E2-4%283%29%28-10%29=169%2B120=289=17%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so your example is factorable.  (If you haven't done the quadratic formula yet, don't worry about it.  Just use the rule above on faith for the time being) </SPAN>\n" );
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