document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=166439>Question 166439</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use synthetic division to show that the number given to the right of the equation is a solution of the equation, then solve the polynomial equation.\r<BR>\n" );
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document.write( "x^3 + 2x^2 - 11x - 12 = 0; -4\r<BR>\n" );
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document.write( "o (3,1,-4)\r<BR>\n" );
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document.write( "o (3,-1,-4)\r<BR>\n" );
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document.write( "o (-3,1,-4)\r<BR>\n" );
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document.write( "o (-3,-1,-4)\r<BR>\n" );
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document.write( "Using a previous example given on this website, I believe the answer is the first choice given above, but am not certain. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #122659 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=122659\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First, substitute x = -4:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-4%29%5E3%2B2%28-4%29%5E2-11%28-4%29-12+=+-64%2B32%2B44-12 ALIGN=MIDDLE  ALT=\"%28-4%29%5E3%2B2%28-4%29%5E2-11%28-4%29-12+=+-64%2B32%2B44-12\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=76-76+=+0 ALIGN=MIDDLE  ALT=\"76-76+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now, if x = -4 is a root, (and it is), then x+4 = 0 and x+4 is a factor of the given cubic equation.<BR>\n" );
document.write( "So when you divide the given equation by the factor (x+4) you get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-2x-3 ALIGN=MIDDLE  ALT=\"x%5E2-2x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > so you now have:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B4%29%28x%5E2-2x-3%29+=+0 ALIGN=MIDDLE  ALT=\"%28x%2B4%29%28x%5E2-2x-3%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the trinomial.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B4%29%28x%2B1%29%28x-3%29+=+0 ALIGN=MIDDLE  ALT=\"%28x%2B4%29%28x%2B1%29%28x-3%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Apply the zero product rule to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-4 ALIGN=MIDDLE  ALT=\"x+=+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-1 ALIGN=MIDDLE  ALT=\"x+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+3 ALIGN=MIDDLE  ALT=\"x+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the solution is:<BR>\n" );
document.write( "(3, -1, -4) which is the second choice in the list of possible solutions.<BR>\n" );
document.write( "This can be verified from the graph of the given equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-5%2C5%2C-25%2C15%2Cx%5E3%2B2x%5E2-11x-12%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-5%2C5%2C-25%2C15%2Cx%5E3%2B2x%5E2-11x-12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );