document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=167735>Question 167735</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A partial solution set is given. Find the complete solution set.\r<BR>\n" );
document.write( "\n" );
document.write( "x^3+3x^2-13x-15=0;{-1} </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #123644 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=123644\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Note: since -1 is a given solution, this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B1 ALIGN=MIDDLE  ALT=\"x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a given factor\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since -1 is a given zero, we can use with synthetic division where -1 is the test zero.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Set up the synthetic division table by placing the test zero in the upper left corner and placing the coefficients of the polynomial to the right of the test zero.<TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >-1</TD><TD >|</TD><TD >1</TD><TD >3</TD><TD >-13</TD><TD >-15</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></TR>\n" );
document.write( "</TABLE>\r<BR>\n" );
document.write( "\n" );
document.write( "Start by bringing down the leading coefficient (it is the coefficient with the highest exponent which is 1)\r<BR>\n" );
document.write( "\n" );
document.write( "<TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >-1</TD><TD >|</TD><TD >1</TD><TD >3</TD><TD >-13</TD><TD >-15</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >1</TD><TD ></TD><TD ></TD><TD ></TD></TR>\n" );
document.write( "</TABLE>\r<BR>\n" );
document.write( "\n" );
document.write( "    Multiply -1 by 1 and place the product (which is -1)  right underneath the second  coefficient (which is 3)\r<BR>\n" );
document.write( "\n" );
document.write( "    <TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >-1</TD><TD >|</TD><TD >1</TD><TD >3</TD><TD >-13</TD><TD >-15</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >-1</TD><TD ></TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >1</TD><TD ></TD><TD ></TD><TD ></TD></TR>\n" );
document.write( "</TABLE>\r<BR>\n" );
document.write( "\n" );
document.write( "    Add -1 and 3 to get 2. Place the sum right underneath -1.\r<BR>\n" );
document.write( "\n" );
document.write( "    <TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >-1</TD><TD >|</TD><TD >1</TD><TD >3</TD><TD >-13</TD><TD >-15</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >-1</TD><TD ></TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >1</TD><TD >2</TD><TD ></TD><TD ></TD></TR>\n" );
document.write( "</TABLE>\r<BR>\n" );
document.write( "\n" );
document.write( "    Multiply -1 by 2 and place the product (which is -2)  right underneath the third  coefficient (which is -13)\r<BR>\n" );
document.write( "\n" );
document.write( "    <TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >-1</TD><TD >|</TD><TD >1</TD><TD >3</TD><TD >-13</TD><TD >-15</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >-1</TD><TD >-2</TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >1</TD><TD >2</TD><TD ></TD><TD ></TD></TR>\n" );
document.write( "</TABLE>\r<BR>\n" );
document.write( "\n" );
document.write( "    Add -2 and -13 to get -15. Place the sum right underneath -2.\r<BR>\n" );
document.write( "\n" );
document.write( "    <TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >-1</TD><TD >|</TD><TD >1</TD><TD >3</TD><TD >-13</TD><TD >-15</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >-1</TD><TD >-2</TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >1</TD><TD >2</TD><TD >-15</TD><TD ></TD></TR>\n" );
document.write( "</TABLE>\r<BR>\n" );
document.write( "\n" );
document.write( "    Multiply -1 by -15 and place the product (which is 15)  right underneath the fourth  coefficient (which is -15)\r<BR>\n" );
document.write( "\n" );
document.write( "    <TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >-1</TD><TD >|</TD><TD >1</TD><TD >3</TD><TD >-13</TD><TD >-15</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >-1</TD><TD >-2</TD><TD >15</TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >1</TD><TD >2</TD><TD >-15</TD><TD ></TD></TR>\n" );
document.write( "</TABLE>\r<BR>\n" );
document.write( "\n" );
document.write( "    Add 15 and -15 to get 0. Place the sum right underneath 15.\r<BR>\n" );
document.write( "\n" );
document.write( "    <TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >-1</TD><TD >|</TD><TD >1</TD><TD >3</TD><TD >-13</TD><TD >-15</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >-1</TD><TD >-2</TD><TD >15</TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >1</TD><TD >2</TD><TD >-15</TD><TD >0</TD></TR>\n" );
document.write( "</TABLE>\r<BR>\n" );
document.write( "\n" );
document.write( "Since the last column adds to zero, we have a remainder of zero. This means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B1 ALIGN=MIDDLE  ALT=\"x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a factor of  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+%2B+3x%5E2+-+13x+-+15 ALIGN=MIDDLE  ALT=\"x%5E3+%2B+3x%5E2+-+13x+-+15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now lets look at the bottom row of coefficients:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The first 3 coefficients (1,2,-15) form the quotient\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+2x+-+15 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+2x+-+15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E3+%2B+3x%5E2+-+13x+-+15%29%2F%28x%2B1%29=x%5E2+%2B+2x+-+15 ALIGN=MIDDLE  ALT=\"%28x%5E3+%2B+3x%5E2+-+13x+-+15%29%2F%28x%2B1%29=x%5E2+%2B+2x+-+15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Basically  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+%2B+3x%5E2+-+13x+-+15 ALIGN=MIDDLE  ALT=\"x%5E3+%2B+3x%5E2+-+13x+-+15\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29%28x%5E2+%2B+2x+-+15%29 ALIGN=MIDDLE  ALT=\"%28x%2B1%29%28x%5E2+%2B+2x+-+15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now simply solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+2x+-+15=0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+2x+-+15=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > to find the remaining two solutions (I'll let you do that)<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );