document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=582095>Question 582095</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help factoring.  I just don't get it.\r<BR>\n" );
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document.write( "8x^2y+34xy-84y </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #372004 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=372004\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First you can factor out 2y:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 2y(4x^2 + 17x - 42)\">\r<BR>\n" );
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document.write( "The 4x^2 + 17x - 42 is a bit tricky to factor; the best way to learn is by experience and simply being able to \"see\" the correct factorization.\r<BR>\n" );
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document.write( "4x^2 + 17x - 42 can be factored into a product (ax + b)(cx + d). We want ac = 4, so a,c can equal 2 or 1,4. However, if a = c = +/- 2, the x coefficient will be even, so try a=1, c=4. We can kind of \"guess and check\" based on the factorization of -42 to obtain the factorization\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE (x + 6)(4x - 7)\">, in which the complete answer would be <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 2y(x+6)(4x-7)\">.\r<BR>\n" );
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document.write( "Again, this takes lots of practice. Another way you could factor it is to find the roots of 4x^2 + 17x - 42 by the quadratic formula:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x = \frac{-17 \pm \sqrt{961}}{8} = \frac{7}{2}, -6\">\r<BR>\n" );
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document.write( "Then you could factor it as <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE (x - \frac{7}{2})(x + 6)\">. However, the leading coefficient is 4 so we can multiply the first term by 4. </SPAN>\n" );
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