document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=855004>Question 855004</A>: <I><SPAN STYLE=\"word-break: break-all;\"> i am helping my daughter with her homework and we are both stumped...she got to the last question...i think i know the answer and she doesnt but i dont now how i know...just a guess and would like to review with her the process...Here we go the length of a rectangular area rug is given by the trinomial c^2 - 8c -48 and length is(c-12) find the width...she has tried several ways and none make sense...please help us... i will review with her...need the steps...i think it is c-4 but dont know how to get it...she thinks she needs to factor the trinomial<BR>\n" );
document.write( "This is our first time using...great site<BR>\n" );
document.write( "Thanks in advance </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #515035 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=515035\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Factoring the trinomial could help ---- IF it is factorabale.  \r<BR>\n" );
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document.write( "Area is Length multiplied by Width.  You already seem to understand that.<BR>\n" );
document.write( "Abbreviating with your variables, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=c%5E2-8c-48 ALIGN=MIDDLE  ALT=\"A=c%5E2-8c-48\"   DISABLED_style= \"max-width:90%; height:auto;\" > and you have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=c-12 ALIGN=MIDDLE  ALT=\"L=c-12\"   DISABLED_style= \"max-width:90%; height:auto;\" >; and you want w.  I am using w as width.\r<BR>\n" );
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document.write( "Using formula for area knowledge, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%2Aw=A ALIGN=MIDDLE  ALT=\"L%2Aw=A\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Further using your variable expressions,...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28c-12%29%2Aw=c%5E2-8c-48 ALIGN=MIDDLE  ALT=\"%28c-12%29%2Aw=c%5E2-8c-48\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Is the trinomial easily factorable?  IS it factorable?<BR>\n" );
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document.write( "Let us try to factor the trinomial for the area:<BR>\n" );
document.write( "We want two numbers so that their sum is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8 ALIGN=MIDDLE  ALT=\"-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and their product is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-48 ALIGN=MIDDLE  ALT=\"-48\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  What combinations can we try?<BR>\n" );
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document.write( "48=12*4, MAYBE this will work (there are other combinations).<BR>\n" );
document.write( "(c__12)(c__4)=... we do not yet know the signs.<BR>\n" );
document.write( "12*4=48, but we want NEGATIVE 48.<BR>\n" );
document.write( "12c and 4c can give 8c, but which sign to which in each binomial?.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28c%2B12%29%28c-4%29=c%5E2%2B12c-4c-48 ALIGN=MIDDLE  ALT=\"%28c%2B12%29%28c-4%29=c%5E2%2B12c-4c-48\"   DISABLED_style= \"max-width:90%; height:auto;\" >... NOT what we want, but we are near.<BR>\n" );
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document.write( "Trying the signs the other way:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%28c-12%29%28c%2B4%29=c%5E2-12c%2B4c-48=c%5E2-8c-48%29 ALIGN=MIDDLE  ALT=\"highlight%28%28c-12%29%28c%2B4%29=c%5E2-12c%2B4c-48=c%5E2-8c-48%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >----That is what we want.\r<BR>\n" );
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document.write( "You can now identify the width expression, w, directly from the multiplication there.  The area is the trinomial product way on the right hand side.  The far left hand side shows the length c-12, multiplied by the width, c+4.<BR>\n" );
document.write( "ANSWER: The width, w, is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28highlight%28c%2B4%29%29 ALIGN=MIDDLE  ALT=\"highlight%28highlight%28c%2B4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "ADDITIONALLY, you can actually try <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=A%2FL ALIGN=MIDDLE  ALT=\"w=A%2FL\"   DISABLED_style= \"max-width:90%; height:auto;\" >, using polynomial division, which is really no trouble here, and will give the same result as found.  That means, divide the area <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2-8c-48 ALIGN=MIDDLE  ALT=\"c%5E2-8c-48\"   DISABLED_style= \"max-width:90%; height:auto;\" >, by the length <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c-12 ALIGN=MIDDLE  ALT=\"c-12\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  The quotient will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%2B4 ALIGN=MIDDLE  ALT=\"c%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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