document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=712235>Question 712235</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Do you think you could help me with this?\r<BR>\n" );
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document.write( "Bricks are delivered to a work site and stacked in rows and columns, forming a rectangular prism. The length of the prism is 1 foot greater than its width, and its height is 2 feet less than its width. Show how to find the dimensions of the prism formed by the bricks, given that its volume is 40 cubic feet. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #437852 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=437852\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The unknown being referenced is the width.  \r<BR>\n" );
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document.write( "Let w be width<BR>\n" );
document.write( "Length is w+1<BR>\n" );
document.write( "Height is w-2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%28w%2B1%29%28w-2%29=40 ALIGN=MIDDLE  ALT=\"w%28w%2B1%29%28w-2%29=40\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Some steps,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%28w%5E2%2Bw-2w-2%29-40=0 ALIGN=MIDDLE  ALT=\"w%28w%5E2%2Bw-2w-2%29-40=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "w(w^2-w-2)-40=0<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5E3-w%5E2-2w-40=0 ALIGN=MIDDLE  ALT=\"w%5E3-w%5E2-2w-40=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solving that is faster if you know synthetic division.  You would use the idea of the Rational Roots Theorem to find values for w to satisfy the cubic equation.  I'd suggest first working with +/-4, +/-5, +/-8, +/-10.   When you get just one first root, the next two will be easy.\r<BR>\n" );
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document.write( "Some further work:<BR>\n" );
document.write( "Good News!  I tried some long divisions and found +5 or -5 are not roots, but that +4 is a root.  One of the binomials is (w-4).  The quotient from this was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5E2%2B3w%2B10 ALIGN=MIDDLE  ALT=\"w%5E2%2B3w%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  So this means your polynomial equation is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28w-4%29%28w%5E2%2B3w%2B10%29=0 ALIGN=MIDDLE  ALT=\"%28w-4%29%28w%5E2%2B3w%2B10%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so the quadratic part should be much easier to manage.\r<BR>\n" );
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document.write( "NOTE: The discriminant for that quadratic is -31, so the solution will contain an imaginary part.  The only reasonable value for w is 4. </SPAN>\n" );
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