document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=997336>Question 997336</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If you know that -2 is a zero of f(x)=x^3+7x^2+4x-12, explain how to solve the equation x^3+7x^2+4x+12=0. <BR>\n" );
document.write( "Also give an explanation to why x-2 is or is not a factor </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #615486 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=615486\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E3%2B7x%5E2%2B4x-12 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E3%2B7x%5E2%2B4x-12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\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=-2 ALIGN=MIDDLE  ALT=\"x%5B1%5D=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a zero, means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E3%2B7x%5E2%2B4x-12 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E3%2B7x%5E2%2B4x-12\"   DISABLED_style= \"max-width:90%; height:auto;\" > is divisible by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-x%5B1%5D=x-%28-2%29=x%2B2 ALIGN=MIDDLE  ALT=\"x-x%5B1%5D=x-%28-2%29=x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >->an explanation to why <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;\" > is not a factor\r<BR>\n" );
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document.write( "use long division:\r<BR>\n" );
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document.write( "---------(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B5x-6 ALIGN=MIDDLE  ALT=\"x%5E2%2B5x-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2 ALIGN=MIDDLE  ALT=\"x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >|<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2B7x%5E2%2B4x-12 ALIGN=MIDDLE  ALT=\"x%5E3%2B7x%5E2%2B4x-12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2B2x%5E2 ALIGN=MIDDLE  ALT=\"x%5E3%2B2x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......subtract<BR>\n" );
document.write( "------------<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2B5x%5E2 ALIGN=MIDDLE  ALT=\"0%2B5x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >......add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x ALIGN=MIDDLE  ALT=\"4x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2%2B4x ALIGN=MIDDLE  ALT=\"5x%5E2%2B4x\"   DISABLED_style= \"max-width:90%; height:auto;\" >......<BR>\n" );
document.write( "------------- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2%2B10x ALIGN=MIDDLE  ALT=\"5x%5E2%2B10x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......subtract<BR>\n" );
document.write( "-------------- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0-6x ALIGN=MIDDLE  ALT=\"0-6x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-12 ALIGN=MIDDLE  ALT=\"-12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6x-12 ALIGN=MIDDLE  ALT=\"-6x-12\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......<BR>\n" );
document.write( "--------------- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6x-12 ALIGN=MIDDLE  ALT=\"-6x-12\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......subtract<BR>\n" );
document.write( "----------------- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......reminder\r<BR>\n" );
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document.write( "so, now we know two factors of given polynomial, and they are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2 ALIGN=MIDDLE  ALT=\"x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B5x-6 ALIGN=MIDDLE  ALT=\"x%5E2%2B5x-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, you have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x%2B2%29%28x%5E2%2B5x-6%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x%2B2%29%28x%5E2%2B5x-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ...now we can factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B5x-6 ALIGN=MIDDLE  ALT=\"x%5E2%2B5x-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > too\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%2B2%29%28x%5E2%2B6x-x-6%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x%2B2%29%28x%5E2%2B6x-x-6%29\"   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=f%28x%29=%28x%2B2%29%28%28x%5E2%2B6x%29-%28x%2B6%29%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x%2B2%29%28%28x%5E2%2B6x%29-%28x%2B6%29%29\"   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=f%28x%29=%28x%2B2%29%28x%28x%2B6%29-%28x%2B6%29%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x%2B2%29%28x%28x%2B6%29-%28x%2B6%29%29\"   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=f%28x%29=%28x%2B2%29%28x-1%29%28x%2B6%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x%2B2%29%28x-1%29%28x%2B6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, zeros are:\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=%28x%2B2%29 ALIGN=MIDDLE  ALT=\"0=%28x%2B2%29\"   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;\" ><BR>\n" );
document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=%28x-1%29 ALIGN=MIDDLE  ALT=\"0=%28x-1%29\"   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;\" ><BR>\n" );
document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=%28x%2B6%29 ALIGN=MIDDLE  ALT=\"0=%28x%2B6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-6 ALIGN=MIDDLE  ALT=\"x=-6\"   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=+graph%28+600%2C+600%2C+-10%2C+10%2C+-15%2C+15%2C+x%5E3%2B7x%5E2%2B4x-12%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-15%2C+15%2C+x%5E3%2B7x%5E2%2B4x-12%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );