document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1036216>Question 1036216</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The polynomial x^3  + 5x^2 - ­57x -­189 expresses the volume, in cubic inches, of a shipping box, and the width is (x+3) in.  If the width of the box is 15 in., what are the other two dimensions? ( Hint: The height is greater than the depth.)<BR>\n" );
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document.write( "  A.<BR>\n" );
document.write( "height: 19 in.\r<BR>\n" );
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document.write( "depth: 5 in\r<BR>\n" );
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document.write( "  B.<BR>\n" );
document.write( " height: 21 in.\r<BR>\n" );
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document.write( "depth: 5 in. \r<BR>\n" );
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document.write( "  C.<BR>\n" );
document.write( " height: 19 in.<BR>\n" );
document.write( "depth: 7 in.<BR>\n" );
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document.write( "  D.<BR>\n" );
document.write( " height: 21 in.<BR>\n" );
document.write( "depth: 7 in. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #650880 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=650880\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use <a  rel=nofollow HREF= \"http://calc101.com/webMathematica/long-divide.jsp\">polynomial division</a> to divide <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+%2B+5x%5E2+-+57x+-+189 ALIGN=MIDDLE  ALT=\"x%5E3+%2B+5x%5E2+-+57x+-+189\"   DISABLED_style= \"max-width:90%; height:auto;\" > over <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B5 ALIGN=MIDDLE  ALT=\"x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > to find that\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E3+%2B+5x%5E2+-+57x+-+189%29%2F%28x%2B3%29=x%5E2%2B2x-63 ALIGN=MIDDLE  ALT=\"%28x%5E3+%2B+5x%5E2+-+57x+-+189%29%2F%28x%2B3%29=x%5E2%2B2x-63\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2x-63 ALIGN=MIDDLE  ALT=\"x%5E2%2B2x-63\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B9%29%28x-7%29 ALIGN=MIDDLE  ALT=\"%28x%2B9%29%28x-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So all this means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+%2B+5x%5E2+-+57x+-+189 ALIGN=MIDDLE  ALT=\"x%5E3+%2B+5x%5E2+-+57x+-+189\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29%28x%2B9%29%28x-7%29 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%28x%2B9%29%28x-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "where\r<BR>\n" );
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document.write( "width = x+3<BR>\n" );
document.write( "height = x+9<BR>\n" );
document.write( "depth = x-7\r<BR>\n" );
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document.write( "The height is greater than the depth (given in instructions) so because x+9 is larger than x-7, this tells us which expressions go where.\r<BR>\n" );
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document.write( "We're given <font color=blue>\"the width is (x+3) in....the width of the box is 15 in\"</font> which means\r<BR>\n" );
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document.write( "x+3 = 15<BR>\n" );
document.write( "x+3-3 = 15-3<BR>\n" );
document.write( "x = 12\r<BR>\n" );
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document.write( "Now we finally know the value of x. We can use this to find the other dimensions.\r<BR>\n" );
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document.write( "width = x+3 = 12+3 = 15<BR>\n" );
document.write( "height = x+9 = 12+9 = 21<BR>\n" );
document.write( "depth = x-7 = 12-7 = 5\r<BR>\n" );
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document.write( "The three dimensions of this shipping box are<BR>\n" );
document.write( "width = 15 inches<BR>\n" );
document.write( "height = 21 inches<BR>\n" );
document.write( "depth = 5 inches\r<BR>\n" );
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document.write( "Final Answer: \r<BR>\n" );
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document.write( "B.<BR>\n" );
document.write( "height: 21 in. <BR>\n" );
document.write( "depth: 5 in. <BR>\n" );
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