document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1155004>Question 1155004</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the equation 15x^3+14x^2-3x-2=0given that -1 is a zero of f(x)15x^3+14x^2-3x-2=0\r<BR>\n" );
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document.write( "where does the (x+1) come from? \r<BR>\n" );
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document.write( "what is the best way to solve \r<BR>\n" );
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document.write( "15x^3+14x^2-3x-2=0<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #777545 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=777545\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15x%5E3%2B14x%5E2-3x-2=0 ALIGN=MIDDLE  ALT=\"15x%5E3%2B14x%5E2-3x-2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "given that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a zero of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=15x%5E3%2B14x%5E2-3x-2=0 ALIGN=MIDDLE  ALT=\"f%28x%29=15x%5E3%2B14x%5E2-3x-2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "recall zero product theorem:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D ALIGN=MIDDLE  ALT=\"x%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D ALIGN=MIDDLE  ALT=\"x%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B3%5D ALIGN=MIDDLE  ALT=\"x%5B3%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > are zeros\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=-1 ALIGN=MIDDLE  ALT=\"x%5B1%5D=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a zero, than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-x%5B1%5D%29=x-%28-1%29=x%2B1 ALIGN=MIDDLE  ALT=\"%28x-x%5B1%5D%29=x-%28-1%29=x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >  \r<BR>\n" );
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document.write( "that is where the (x+1) comes from, and it means that  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15x%5E3%2B14x%5E2-3x-2=0 ALIGN=MIDDLE  ALT=\"15x%5E3%2B14x%5E2-3x-2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > is divisible by <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;\" > or <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 one of the factors \r<BR>\n" );
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document.write( " the best way to solve is try to factor completely\r<BR>\n" );
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document.write( "since you know <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, try to make  groups that will factor out <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;\" >  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15x%5E3%2B14x%5E2-3x-2=0 ALIGN=MIDDLE  ALT=\"15x%5E3%2B14x%5E2-3x-2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >......write <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14x%5E2 ALIGN=MIDDLE  ALT=\"14x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%5E2%2B15x%5E2 ALIGN=MIDDLE  ALT=\"-x%5E2%2B15x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x ALIGN=MIDDLE  ALT=\"-3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x-x ALIGN=MIDDLE  ALT=\"-2x-x\"   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=15x%5E3-x%5E2%2B15x%5E2-2x-x-2=0 ALIGN=MIDDLE  ALT=\"15x%5E3-x%5E2%2B15x%5E2-2x-x-2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >...group\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2815x%5E3%2B15x%5E2%29-%28x%5E2%2Bx%29-%282x%2B2%29=0 ALIGN=MIDDLE  ALT=\"%2815x%5E3%2B15x%5E2%29-%28x%5E2%2Bx%29-%282x%2B2%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=15x%5E2%28x%2B1%29-x%28x%2B1%29-2%28x%2B1%29=0 ALIGN=MIDDLE  ALT=\"15x%5E2%28x%2B1%29-x%28x%2B1%29-2%28x%2B1%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=%28x+%2B+1%29%2815x%5E2+-+x+-+2%29+=+0 ALIGN=MIDDLE  ALT=\"%28x+%2B+1%29%2815x%5E2+-+x+-+2%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=%28x+%2B+1%29%2815x%5E2+%2B5x+-+6x+-+2%29+=+0 ALIGN=MIDDLE  ALT=\"%28x+%2B+1%29%2815x%5E2+%2B5x+-+6x+-+2%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=%28x+%2B+1%29%28%2815x%5E2+%2B5x%29+-+%286x+%2B+2%29%29+=+0 ALIGN=MIDDLE  ALT=\"%28x+%2B+1%29%28%2815x%5E2+%2B5x%29+-+%286x+%2B+2%29%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=%28x+%2B+1%29%285x%283x+%2B1%29+-+2%283x+%2B+1%29%29+=+0 ALIGN=MIDDLE  ALT=\"%28x+%2B+1%29%285x%283x+%2B1%29+-+2%283x+%2B+1%29%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=%28x+%2B+1%29%283x+%2B+1%29%285x-2%29+=+0 ALIGN=MIDDLE  ALT=\"%28x+%2B+1%29%283x+%2B+1%29%285x-2%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "now, find solutions\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+1%29+=+0 ALIGN=MIDDLE  ALT=\"%28x+%2B+1%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><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;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x+%2B+1%29=+0 ALIGN=MIDDLE  ALT=\"%283x+%2B+1%29=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x=-1 ALIGN=MIDDLE  ALT=\"3x=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1%2F3 ALIGN=MIDDLE  ALT=\"x=-1%2F3\"   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=%285x-2%29+=+0 ALIGN=MIDDLE  ALT=\"%285x-2%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x=2 ALIGN=MIDDLE  ALT=\"5x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2%2F5 ALIGN=MIDDLE  ALT=\"x=2%2F5\"   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=drawing+%28+600%2C+600%2C+-5%2C+5%2C+-5%2C+5%2C%0D%0Acircle%28-1%2C0%2C.08%29%2Ccircle%28-1%2F3%2C0%2C.08%29%2Ccircle%282%2F5%2C0%2C.08%29%2C%0D%0Agraph%28+600%2C+600%2C+-5%2C+5%2C+-5%2C+5%2C+15x%5E3%2B14x%5E2-3x-2%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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