document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=251549>Question 251549</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A cubic shipping container had a volume of v3 cubic meters. The height of the container was decreased by a whole number of meters and the width was increased by a whole number of meters so that the volume of the container is now v3 + 2v2 – 3v. Find out the following:\r<BR>\n" );
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document.write( "a.	By how many meters the height was decreased?\r<BR>\n" );
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document.write( "b.	By how many meters the width was increased?  <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #183339 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=183339\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> v[1] = v^3\r<BR>\n" );
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document.write( "v[2] = v^3 + 2v^2 - 3v\r<BR>\n" );
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document.write( "let a = amount height was decreased.<BR>\n" );
document.write( "let b = amount width was increased.\r<BR>\n" );
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document.write( "v * (v-a) * (v+b) = v^3 + 2v^2 - 3v.\r<BR>\n" );
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document.write( "find the roots of v^3 + 2v^2 - 3v.\r<BR>\n" );
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document.write( "set the equation equal to 0 to get:\r<BR>\n" );
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document.write( "v^3 + 2v^2 - 3v = 0\r<BR>\n" );
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document.write( "factor out a v to get:\r<BR>\n" );
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document.write( "v * (v^2 + 2v - 3) = 0\r<BR>\n" );
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document.write( "factor v^2 + 2v - 3 to get:\r<BR>\n" );
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document.write( "(v-1) * (v+3) * v = 0\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "a = 1<BR>\n" );
document.write( "b = 3\r<BR>\n" );
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document.write( "confirm by substituting in original equation to get:\r<BR>\n" );
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document.write( "v * (v-1) * (v+3) = (v^2 -v) * (v+3) = v^3 + 3v^2 -v^2 - 3v.\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "v * (v-1) * (v+3) = v^3 + 2v^2 - 3v\r<BR>\n" );
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document.write( "since this is identical to the original equation of v^3 + 2v^2 - 3v, then the values for a and b are good.\r<BR>\n" );
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document.write( "v*v*v = v^3 = original equation for the cube.\r<BR>\n" );
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document.write( "v*(v-1)*(v+3) = v^3 + 2v^2 - 3v = original equation after taking 1 unit off the length and adding 3 units to the width.\r<BR>\n" );
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document.write( "answer is:\r<BR>\n" );
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document.write( "height was decreased by 1 unit.<BR>\n" );
document.write( "width was increased by 3 units.\r<BR>\n" );
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