document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=190084>Question 190084</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Factor each trinomial.  10w^2-19w-15   I can not get this. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #142642 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=142642\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "You can go through the process of finding all of the possible factors of -15 and 10, blah blah blah, but there is a much simpler and quicker method.  Use the idea that if <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x = a\"> is a root of the equation formed when you set the polynomial equal to zero, then <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x - a\"> must be a factor of the polynomial.  Since this is a quadratic trinomial, you can set it equal to zero and use the quadratic formula to find the roots -- then the factors become obvious.\r<BR>\n" );
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document.write( "Step 1:  Set the trinomial equal to zero.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  10w^2-19w-15=0\">\r<BR>\n" );
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document.write( "Step 2: Solve with the quadratic formula:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ w = \frac{-b \pm sqrt{b^2 - 4ac}}{2a} = \frac{-(-19) \pm sqrt{(-19)^2 - 4(10)(-15)}}{2(10)} = \frac{19 \pm sqrt{961}}{20} = \frac{19 \pm 31}{20} \">\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/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  w = \frac{19 + 31}{20} = \frac{50}{20} =\frac{5}{2} \ \ \Rightarrow\ \ 2w - 5 = 0\">\r<BR>\n" );
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document.write( "Or\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  w = \frac{19 - 31}{20} = \frac{-12}{20} =\frac{-3}{5} \ \ \Rightarrow\ \ 5w + 3 = 0\">\r<BR>\n" );
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document.write( "Verifying that\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (2w - 5)(5w + 3) = 10w^2-19w-15\">\r<BR>\n" );
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document.write( "is left as an exercise for the student.\r<BR>\n" );
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document.write( "By the way, if you end up with a pair irrational roots, then the trinomial is not factorable over the rational numbers.\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" );
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