document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1122314>Question 1122314</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 9. The polynomial -x^3 -x^2 + 12x  represents the volume of a rectangular aquatic tank in cubic feet. The length of the tank is (x + 4).  \r<BR>\n" );
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document.write( "a.  Use synthetic division to help you factor the volume of the polynomial.  How many linear factors should you look for? \r<BR>\n" );
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document.write( "b. What are the dimensions of the tank?  \r<BR>\n" );
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document.write( "c. Find the value of x that will maximize the volume of the box. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #738396 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</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=738396\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Volumes are not negative.\r<BR>\n" );
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document.write( "The polynomial -x^3 -x^2 + 12x represents the volume of a rectangular aquatic tank in cubic feet. ...<BR>\n" );
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document.write( "If what you wrote is the way it was given to you, then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-x%5E3-x%5E2%2B12x%29%2F%28x%2B4%29 ALIGN=MIDDLE  ALT=\"%28-x%5E3-x%5E2%2B12x%29%2F%28x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%2Ax%28x%5E2%2Bx-12%29%29%2F%28x%2B4%29 ALIGN=MIDDLE  ALT=\"%28-1%2Ax%28x%5E2%2Bx-12%29%29%2F%28x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and the division you want to perform as synthetic division is, as if you were checking root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4 ALIGN=MIDDLE  ALT=\"-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "-4  |  1  1  -12\r\n" );
document.write( "    |    -4   12\r\n" );
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document.write( "       1  -3  0\r\n" );
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document.write( "This is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3 ALIGN=MIDDLE  ALT=\"x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The factorization of the volume expression is then  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28-1%2Ax%28x%2B4%29%28x-3%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%28-1%2Ax%28x%2B4%29%28x-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Note, there are three real roots for -x^3-x^2+12x, and you should expect positive values for the volume to be somewhere on the positive x-axis.\r<BR>\n" );
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document.write( "-\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28d%2Fdx%29%28-x%5E3-x%5E2%2B12x%29 ALIGN=MIDDLE  ALT=\"%28d%2Fdx%29%28-x%5E3-x%5E2%2B12x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x%5E2-2x%2B12 ALIGN=MIDDLE  ALT=\"-3x%5E2-2x%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x%5E2-2x%2B12=0 ALIGN=MIDDLE  ALT=\"-3x%5E2-2x%2B12=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2%2B2x-12=0 ALIGN=MIDDLE  ALT=\"3x%5E2%2B2x-12=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-2%2B-+sqrt%284%2B144%29%29%2F6 ALIGN=MIDDLE  ALT=\"x=%28-2%2B-+sqrt%284%2B144%29%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Must be the positive value.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-2%2B+sqrt%28148%29%29%2F6 ALIGN=MIDDLE  ALT=\"x=%28-2%2B+sqrt%28148%29%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-2%2B2%2Asqrt%2837%29%29%2F%282%2A3%29 ALIGN=MIDDLE  ALT=\"x=%28-2%2B2%2Asqrt%2837%29%29%2F%282%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1%2F3%2Bsqrt%2837%29%2F3 ALIGN=MIDDLE  ALT=\"x=-1%2F3%2Bsqrt%2837%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >-------------------Use this to find the length of x+4; and use x to evaluate the volume there. </SPAN>\n" );
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