document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=835699>Question 835699</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the remainder theorem to find the remainder when f(x) is divided by x+3. Then use the factor theorem to determine whether x+3 is a factor of f(x).\r<BR>\n" );
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document.write( "f(x)=3x^6-27x^4+x^3-5\r<BR>\n" );
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document.write( "a. what is the remainder <BR>\n" );
document.write( "b. Is x+3 a factor of f(x)=3x^6-27^4+x^3-5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #503697 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=503697\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use synthetic division.  If a nonzero remainder, this means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-3%29=theNonZeroRemainder ALIGN=MIDDLE  ALT=\"f%28-3%29=theNonZeroRemainder\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  If remainder is zero, then x+3 is a factor of f(x).\r<BR>\n" );
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document.write( "Checking  -3 as possible zero.\r<BR>\n" );
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document.write( "-3____|_____3____0_____-27____1_____0_____0_____-5<BR>\n" );
document.write( "______|<BR>\n" );
document.write( "______|__________-9____27_____0____-3_____9_____-27<BR>\n" );
document.write( "___________3____-9______0_____1____-3_____9_____<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28highlight%28-32%29%29 ALIGN=MIDDLE  ALT=\"highlight%28highlight%28-32%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The remainder is -32, so this means, x+3 is NOT a factor of f, but that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28f%28-3%29=-32%29 ALIGN=MIDDLE  ALT=\"highlight%28f%28-3%29=-32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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