document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=6613>Question 6613</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having a hard time with Variation, Progression, and Theorems.  My question is Use the remainder theorem to determine the remainder when 5w^3 -2w+10 is divided by w+3?  \r<BR>\n" );
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document.write( "Can someone please help me, I have already tried to answer this question on my own and cannot seem to get the right answer?  Please? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #3624 by </B><A HREF=/tutors/aboutme.mpl?userid=rapaljer><B>rapaljer(4671)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rapaljer><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=rapaljer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=3624\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are two ways to find the remainder after division by a binomial such as w+3.  The first most obvious way is to divide it out, using either long division or synthetic division.  However, according to the Remainder Theorem, if a polynomial P(x) is divided by the binomial x-a, then the remainder is P(a). \r<BR>\n" );
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document.write( "In this case, using the remainder theorem, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28w%29=+5w%5E3+-2w+%2B+10 ALIGN=MIDDLE  ALT=\"P%28w%29=+5w%5E3+-2w+%2B+10\"   DISABLED_style= \"max-width:90%; height:auto;\" > is divided by w+3, where a = -3, so the remainder is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28-3%29+=+5%2A%28-3%29%5E3+-2%2A%28-3%29+%2B+10 ALIGN=MIDDLE  ALT=\"P%28-3%29+=+5%2A%28-3%29%5E3+-2%2A%28-3%29+%2B+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28-3%29+=+5%2A+%28-27%29+%2B+6+%2B+10 ALIGN=MIDDLE  ALT=\"P%28-3%29+=+5%2A+%28-27%29+%2B+6+%2B+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28-3%29+=+-135+%2B+16+=+-119+ ALIGN=MIDDLE  ALT=\"P%28-3%29+=+-135+%2B+16+=+-119+\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  The remainder is -119.\r<BR>\n" );
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document.write( "You can check this by synthetic division.  Write down the coefficients of the polynomial (be sure it is in descending powers of the variable, and if any terms are missing, be sure to put zero for the coefficients of missing terms).\r<BR>\n" );
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document.write( "-3 |   5 `  0  `-2  ` 10<BR>\n" );
document.write( "````` -15  45  -129<BR>\n" );
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document.write( "```  5 -15  43  -119\r<BR>\n" );
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document.write( "The last number is the remainder, -119, so it checks.\r<BR>\n" );
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document.write( "R^2 at SCC\r<BR>\n" );
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document.write( " </SPAN>\n" );
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