document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1185932>Question 1185932</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Factor the polynomial and use the factored form to find the real zeros. (Enter your answers as a comma-separated list. Enter all answers including repetitions.)<BR>\n" );
document.write( "P(x) = 1/6(2x4 + 3x3 − 16x − 24)^2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #816848 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=816848\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29+=+%281%2F6%29%282x%5E4+%2B+3x%5E3-16x-+24%29%5E2 ALIGN=MIDDLE  ALT=\"P%28x%29+=+%281%2F6%29%282x%5E4+%2B+3x%5E3-16x-+24%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F6%29%282x%5E4+%2B+3x%5E3-16x-+24%29%5E2=0+ ALIGN=MIDDLE  ALT=\"%281%2F6%29%282x%5E4+%2B+3x%5E3-16x-+24%29%5E2=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >will be if\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E4+%2B+3x%5E3-16x-+24=0 ALIGN=MIDDLE  ALT=\"2x%5E4+%2B+3x%5E3-16x-+24=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%5E4+%2B+3x%5E3%29-%2816x%2B+24%29=0 ALIGN=MIDDLE  ALT=\"%282x%5E4+%2B+3x%5E3%29-%2816x%2B+24%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%282x+%2B+3%29-8%282x%2B+3%29=0 ALIGN=MIDDLE  ALT=\"x%5E3%282x+%2B+3%29-8%282x%2B+3%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x+%2B+3%29+%28x%5E3+-+8%29+=+0 ALIGN=MIDDLE  ALT=\"%282x+%2B+3%29+%28x%5E3+-+8%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >........use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8=2%5E3 ALIGN=MIDDLE  ALT=\"8=2%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x+%2B+3%29+%28x%5E3+-+2%5E3%29+=+0 ALIGN=MIDDLE  ALT=\"%282x+%2B+3%29+%28x%5E3+-+2%5E3%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > .......use the rule for factoring the difference of the cubes\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B3%29%28x-2%29%28x%5E2%2B2x%2B4%29=0 ALIGN=MIDDLE  ALT=\"%282x%2B3%29%28x-2%29%28x%5E2%2B2x%2B4%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >......... zeros are\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B3%29=0 ALIGN=MIDDLE  ALT=\"%282x%2B3%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3%2F2 ALIGN=MIDDLE  ALT=\"x=-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "if  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29+=0 ALIGN=MIDDLE  ALT=\"%28x-2%29+=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > =><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x=2 ALIGN=MIDDLE  ALT=\"+x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "for<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2%2B2x%2B4=0 ALIGN=MIDDLE  ALT=\"+x%5E2%2B2x%2B4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > use quadratic formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .....in your case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=2 ALIGN=MIDDLE  ALT=\"b=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=4 ALIGN=MIDDLE  ALT=\"c=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-2%2B-sqrt%282%5E2-4%2A1%2A4%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x=%28-2%2B-sqrt%282%5E2-4%2A1%2A4%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-2%2B-sqrt%284-16%29%29%2F2 ALIGN=MIDDLE  ALT=\"x=%28-2%2B-sqrt%284-16%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-2%2B-sqrt%28-12%29%29%2F2 ALIGN=MIDDLE  ALT=\"x=%28-2%2B-sqrt%28-12%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-2%2B-sqrt%28-4%2A3%29%29%2F2 ALIGN=MIDDLE  ALT=\"x=%28-2%2B-sqrt%28-4%2A3%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-2%2B-2sqrt%283%29%2Ai%29%2F2 ALIGN=MIDDLE  ALT=\"x=%28-2%2B-2sqrt%283%29%2Ai%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >........simplify<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-1%2B-sqrt%283%29%2Ai%29 ALIGN=MIDDLE  ALT=\"x=%28-1%2B-sqrt%283%29%2Ai%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "roots: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2Bsqrt%283%29%2Ai ALIGN=MIDDLE  ALT=\"-1%2Bsqrt%283%29%2Ai\"   DISABLED_style= \"max-width:90%; height:auto;\" >,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1-sqrt%283%29%2Ai ALIGN=MIDDLE  ALT=\"-1-sqrt%283%29%2Ai\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "all roots will be\r<BR>\n" );
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document.write( "real roots:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3%2F2 ALIGN=MIDDLE  ALT=\"x=-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "complex roots:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2Bsqrt%283%29%2Ai ALIGN=MIDDLE  ALT=\"-1%2Bsqrt%283%29%2Ai\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-1-sqrt%283%29%2Ai ALIGN=MIDDLE  ALT=\"+-1-sqrt%283%29%2Ai\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );