document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1007663>Question 1007663</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find all the zeros of the function using the Rational Root Theorem \r<BR>\n" );
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document.write( "If       f(x) = x^3-4x^2+11x-9      and            g(x) = x^2-4x-1\r<BR>\n" );
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document.write( "  find f(x)-g(x-1) \r<BR>\n" );
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document.write( "My teacher taught how the rational root theorem I'm just confused on when plugging in g(x-1) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #623491 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=623491\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "If       <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+x%5E3-4x%5E2%2B11x-9 ALIGN=MIDDLE  ALT=\"f%28x%29+=+x%5E3-4x%5E2%2B11x-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >      and            <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29+=+x%5E2-4x-1 ALIGN=MIDDLE  ALT=\"g%28x%29+=+x%5E2-4x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "  find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29-g%28x-1%29 ALIGN=MIDDLE  ALT=\"f%28x%29-g%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >....since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=+x%5E3-4x%5E2%2B11x-9 ALIGN=MIDDLE  ALT=\"f%28x%29=+x%5E3-4x%5E2%2B11x-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > we need <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x-1%29=%28x-1%29%5E2-4%28x-1%29-1 ALIGN=MIDDLE  ALT=\"g%28x-1%29=%28x-1%29%5E2-4%28x-1%29-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then we have:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29-g%28x-1%29=+x%5E3-4x%5E2%2B11x-9-%28x%5E2-2x%2B1-4x%2B4-1%29 ALIGN=MIDDLE  ALT=\"f%28x%29-g%28x-1%29=+x%5E3-4x%5E2%2B11x-9-%28x%5E2-2x%2B1-4x%2B4-1%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-g%28x-1%29=+x%5E3-4x%5E2%2B11x-9-%28x%5E2-6x%2B4%29 ALIGN=MIDDLE  ALT=\"f%28x%29-g%28x-1%29=+x%5E3-4x%5E2%2B11x-9-%28x%5E2-6x%2B4%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-g%28x-1%29=+x%5E3-4x%5E2%2B11x-9-x%5E2%2B6x-4 ALIGN=MIDDLE  ALT=\"f%28x%29-g%28x-1%29=+x%5E3-4x%5E2%2B11x-9-x%5E2%2B6x-4\"   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-g%28x-1%29=+x%5E3-5x%5E2%2B17x-13 ALIGN=MIDDLE  ALT=\"f%28x%29-g%28x-1%29=+x%5E3-5x%5E2%2B17x-13\"   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-g%28x-1%29=+x%5E3-x%5E2-4x%5E2%2B4x%2B13x-13 ALIGN=MIDDLE  ALT=\"f%28x%29-g%28x-1%29=+x%5E3-x%5E2-4x%5E2%2B4x%2B13x-13\"   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-g%28x-1%29=+%28x%5E3-x%5E2%29-%284x%5E2-4x%29%2B%2813x-13%29 ALIGN=MIDDLE  ALT=\"f%28x%29-g%28x-1%29=+%28x%5E3-x%5E2%29-%284x%5E2-4x%29%2B%2813x-13%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-g%28x-1%29=+x%5E2%28x-1%29-4x%28x-1%29%2B13%28x-1%29 ALIGN=MIDDLE  ALT=\"f%28x%29-g%28x-1%29=+x%5E2%28x-1%29-4x%28x-1%29%2B13%28x-1%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-g%28x-1%29=%28x-1%29+%28x%5E2-4x%2B13%29 ALIGN=MIDDLE  ALT=\"f%28x%29-g%28x-1%29=%28x-1%29+%28x%5E2-4x%2B13%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "zeros:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29+%28x%5E2-4x%2B13%29=0 ALIGN=MIDDLE  ALT=\"%28x-1%29+%28x%5E2-4x%2B13%29=0\"   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=%28x-1%29=0 ALIGN=MIDDLE  ALT=\"%28x-1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=1%29 ALIGN=MIDDLE  ALT=\"highlight%28x=1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > real zero \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-4x%2B13%29=0 ALIGN=MIDDLE  ALT=\"%28x%5E2-4x%2B13%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >...since cannot be factored, use quadratic formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%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=x+=+%28-%28-4%29+%2B-+sqrt%28+%28-4%29%5E2-4%2A1%2A13+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-%28-4%29+%2B-+sqrt%28+%28-4%29%5E2-4%2A1%2A13+%29%29%2F%282%2A1%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=x+=+%284+%2B-+sqrt%28+16-52+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%284+%2B-+sqrt%28+16-52+%29%29%2F2+\"   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=x+=+%284+%2B-+sqrt%28+-36+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%284+%2B-+sqrt%28+-36+%29%29%2F2+\"   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=x+=+%284+%2B-+6i+%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%284+%2B-+6i+%29%2F2+\"   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=x+=+%28cross%284%292+%2B-+cross%286%293i+%29%2Fcross%282%29+ ALIGN=MIDDLE  ALT=\"x+=+%28cross%284%292+%2B-+cross%286%293i+%29%2Fcross%282%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=x+=+%282+%2B-+3i+%29+ ALIGN=MIDDLE  ALT=\"x+=+%282+%2B-+3i+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "complex zeros:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x+=+2+%2B+3i%29++ ALIGN=MIDDLE  ALT=\"highlight%28x+=+2+%2B+3i%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=highlight%28x+=+2+-+3i+%29+ ALIGN=MIDDLE  ALT=\"highlight%28x+=+2+-+3i+%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" );