document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=644161>Question 644161</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A large plywood box has a volume of 12 ft3. Its length is 4 ft greater than its height, and its width is 1 ft less than its height. What are the dimensions 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 #404858 by </B><A HREF=/tutors/aboutme.mpl?userid=DrBeeee><B>DrBeeee(684)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=DrBeeee><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=404858\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use the formula<BR>\n" );
document.write( "(1) V = lwh<BR>\n" );
document.write( "with<BR>\n" );
document.write( "(2) l = h + 4<BR>\n" );
document.write( "(3) w = h - 1<BR>\n" );
document.write( "to obtain<BR>\n" );
document.write( "(4) (h + 4 )(h - 1)h = 12<BR>\n" );
document.write( "Simplify to<BR>\n" );
document.write( "(5) (h^2 + 3h - 4)h - 12 = 0 or<BR>\n" );
document.write( "(6) h^3 + 3h^2 - 4h - 12 = 0<BR>\n" );
document.write( "Since all cubic equations have one real root, find it first by substituting different values of h into (6) until (6) = 0. <BR>\n" );
document.write( "I start at h=0, then <BR>\n" );
document.write( "f(0) = -12<BR>\n" );
document.write( "f(1) = 1+3-4-12 = -12<BR>\n" );
document.write( "f(2) = 8+12-8-12 = 0, STOP<BR>\n" );
document.write( "Therefore h = 2 is a root or<BR>\n" );
document.write( "(7) (h-2) is a factor of (6).<BR>\n" );
document.write( "To find the other roots divide (6) by (7) to obtain<BR>\n" );
document.write( "(8) h^2+5h+6 = 0<BR>\n" );
document.write( "Factor (8) to obtain<BR>\n" );
document.write( "(9) (h+2)(h+3) = 0<BR>\n" );
document.write( "which gives the roots<BR>\n" );
document.write( "(10) h = {-2,-3}<BR>\n" );
document.write( "Since both are negative, they cannot be the height of the box.<BR>\n" );
document.write( "Our answer is<BR>\n" );
document.write( "(11) h = 2,<BR>\n" );
document.write( "and from (2) and (3) we get<BR>\n" );
document.write( "(12) l = 6 and<BR>\n" );
document.write( "(13) w = 1<BR>\n" );
document.write( "Is (lwh = 12)?<BR>\n" );
document.write( "Is (6*1*2 = 12)<BR>\n" );
document.write( "Is ( 12 = 12)? Yes<BR>\n" );
document.write( "Answer: The box is 6ft by 1ft by 2ft.<BR>\n" );
document.write( "We can also check our factoring of (6) by FOILing<BR>\n" );
document.write( "(14) (h-2)(h+2)(h+3) =<BR>\n" );
document.write( "(15) (h^2 - 4)(h+3) =<BR>\n" );
document.write( "(16) h^3 - 4h + 3h^2 - 12 =<BR>\n" );
document.write( "(17) h^3 + 3h^2 - 4h - 12<BR>\n" );
document.write( "Which is the same as (6). </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );