document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=119703>Question 119703</A>: <I><SPAN STYLE=\"word-break: break-all;\"> factor completely  -3t^3+3t^2-6t </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #87705 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=87705\">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=-3t%5E3%2B3t%5E2-6t ALIGN=MIDDLE  ALT=\"-3t%5E3%2B3t%5E2-6t\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3t%28t%5E2-t%2B2%29 ALIGN=MIDDLE  ALT=\"-3t%28t%5E2-t%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the GCF <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3t ALIGN=MIDDLE  ALT=\"-3t\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now let's focus on the inner expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5E2-t%2B2 ALIGN=MIDDLE  ALT=\"t%5E2-t%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Looking at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5E2-t%2B2 ALIGN=MIDDLE  ALT=\"t%5E2-t%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > we can see that the first term is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5E2 ALIGN=MIDDLE  ALT=\"t%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the last term is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > where the coefficients are 1 and 2 respectively.\r<BR>\n" );
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document.write( "Now multiply the first coefficient 1 and the last coefficient 2 to get 2. Now what two numbers multiply to 2 and add to the  middle coefficient -1? Let's list all of the factors of 2:\r<BR>\n" );
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document.write( "Factors of 2:\r<BR>\n" );
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document.write( "1,2\r<BR>\n" );
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document.write( "-1,-2 ...List the negative factors as well. This will allow us to find all possible combinations\r<BR>\n" );
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document.write( "These factors pair up and multiply to 2\r<BR>\n" );
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document.write( "1*2\r<BR>\n" );
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document.write( "(-1)*(-2)\r<BR>\n" );
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document.write( "note: remember two negative numbers multiplied together make a positive number\r<BR>\n" );
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document.write( "Now which of these pairs add to -1? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -1\r<BR>\n" );
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document.write( "<th>First Number</th><th>Second Number</th><th>Sum</th><tr><TD  align=\"center\">1</TD><TD  align=\"center\">2</TD><TD >1+2=3</TD></tr><tr><TD  align=\"center\">-1</TD><TD  align=\"center\">-2</TD><TD >-1+(-2)=-3</TD></tr>\n" );
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document.write( "None of these pairs of factors add to -1. So the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5E2-t%2B2 ALIGN=MIDDLE  ALT=\"t%5E2-t%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > cannot be factored\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3t%5E3%2B3t%5E2-6t ALIGN=MIDDLE  ALT=\"-3t%5E3%2B3t%5E2-6t\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3t%28t%5E2-t%2B2%29 ALIGN=MIDDLE  ALT=\"-3t%28t%5E2-t%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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