document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1141800>Question 1141800</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (a) The volume of a box is represented by the function, V(x)=x^3+5x^2+2x-8.<BR>\n" );
document.write( "If the height of the box is represented by (x+4), determine the possible dimensions(binomials) of the box. Is there any restriction on the value of x? <BR>\n" );
document.write( "(b) If the volume of the box is 70cm^3  determine possible whole number value(s) for x.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #762444 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13215)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=762444\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "(a) The volume of the box is length times width times height; you are given that the height is x+4.<br><BR>\n" );
document.write( "(1) Use synthetic division to remove the factor (x+4).<br><PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "\r\n" );
document.write( "  -4 |  1   5   2  -8\r\n" );
document.write( "     |     -4  -4   8\r\n" );
document.write( "     +-----------------\r\n" );
document.write( "        1   1  -2   0</PRE><BR>\n" );
document.write( "So<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2B5x%5E2%2B2x-8+=+%28x%2B4%29%28x%5E2%2Bx-2%29 ALIGN=MIDDLE  ALT=\"x%5E3%2B5x%5E2%2B2x-8+=+%28x%2B4%29%28x%5E2%2Bx-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "(2) Factor the quadratic.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2B5x%5E2%2B2x-8+=+%28x%2B4%29%28x%2B2%29%28x-1%29 ALIGN=MIDDLE  ALT=\"x%5E3%2B5x%5E2%2B2x-8+=+%28x%2B4%29%28x%2B2%29%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: The possible dimensions of the box are (x-1), (x+2), and (x+4).  Since dimensions of a box must be positive, the restriction is that x has to be greater than 1.<br><BR>\n" );
document.write( "(b) You could use any number of methods to solve the equation<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2B5x%5E2%2B2x-8+=+70 ALIGN=MIDDLE  ALT=\"x%5E3%2B5x%5E2%2B2x-8+=+70\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "However, since we know x > 1 and we are looking for whole number values for x, we can quickly find the solution by logical trial and error.<br><BR>\n" );
document.write( "x=2: (x-1)(x+2)(x+4) = (1)(4)(6) = 24  no...<br><BR>\n" );
document.write( "x=3: (x-1)(x+2)(x+4) = (2)(5)(7) = 70  YES!<br><BR>\n" );
document.write( "And clearly larger values of x will produce volumes greater than 70.<br><BR>\n" );
document.write( "ANSWER: x=3 makes the volume 70 </SPAN>\n" );
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