document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1049291>Question 1049291</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The product of four consecutive natural numbers is 1680 find the numbers </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #664832 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</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=664832\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You would expect them all to be near 10 each, not exactly.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2A%28n%2B1%29%28n%2B2%29%28n%2B3%29=1680 ALIGN=MIDDLE  ALT=\"n%2A%28n%2B1%29%28n%2B2%29%28n%2B3%29=1680\"   DISABLED_style= \"max-width:90%; height:auto;\" >, should not be as bad as it looks because the product being four digits, each of the factors or consecutive natural numbers, should be of one or two digit.  Consider 10*10*10*10=1000, only \" a little smaller than \" your product 1680.  Ten is probably one of the numbers.\r<BR>\n" );
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document.write( "Simplify to obtain  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E4%2B6n%5E3%2B11n%5E2%2B6n-1680 ALIGN=MIDDLE  ALT=\"n%5E4%2B6n%5E3%2B11n%5E2%2B6n-1680\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The factorizations of 1680?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=168%2A10=2%2A7%2A12%2A10 ALIGN=MIDDLE  ALT=\"168%2A10=2%2A7%2A12%2A10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Listing some pairs of factorizations of 1680:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%282%2A840%2C4%2A420%2C5%2A336%2C6%2A280%2C7%2A240%2C8%2A210%2C9%2AnoneWhole%29 ALIGN=MIDDLE  ALT=\"system%282%2A840%2C4%2A420%2C5%2A336%2C6%2A280%2C7%2A240%2C8%2A210%2C9%2AnoneWhole%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Using synthetic division, start with 8 and work downward to check for roots.\r<BR>\n" );
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document.write( "Only one whole number from 2 to 8 seems to work as a rational root, positive values.<BR>\n" );
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document.write( "5    |    1   6   11   6   -1680\r\n" );
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document.write( "     |        5   55   330   1680\r\n" );
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document.write( "          1  11   66  336     0\r\n" );
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document.write( "You could continue on to check 1 and the negative values between negative 1 and negative 9 as possible roots, but see what we have if n=5.\r<BR>\n" );
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document.write( "<b>The consecutive whole number factors are  5, 6, 7, 8.</b><BR>\n" );
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document.write( "CHECK:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A6%2A7%2A8=40%2A42=1680 ALIGN=MIDDLE  ALT=\"5%2A6%2A7%2A8=40%2A42=1680\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OKAY. </SPAN>\n" );
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