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 #3625 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=3625\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The remainder theorem states: \r<BR>\n" );
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document.write( "If a polynomial P(x) is divided by (x-a), where a is a constant, then the remainder is P(a).\r<BR>\n" );
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document.write( "Starting with your polynomial: <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;\" > and the given divisor: (w+3), you should be able to find the remainder by noting that, in this case, a = -3.\r<BR>\n" );
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document.write( "The remainder then should be P(-3) Let's find out.\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+=+%285%28-3%29%5E3+-+2%28-3%29+%2B+10%29 ALIGN=MIDDLE  ALT=\"P%28-3%29+=+%285%28-3%29%5E3+-+2%28-3%29+%2B+10%29\"   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+=+%285%28-27%29+%2B+6+%2B+10%29 ALIGN=MIDDLE  ALT=\"P%28-3%29+=+%285%28-27%29+%2B+6+%2B+10%29\"   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+=+%28-135+%2B+16%29 ALIGN=MIDDLE  ALT=\"P%28-3%29+=+%28-135+%2B+16%29\"   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+=+-119 ALIGN=MIDDLE  ALT=\"P%28-3%29+=+-119\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "To check this solution, you will need to perform the division, either by long division or by synthetic division.\r<BR>\n" );
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document.write( "I have done this and indeed, -119 is the remainder after dividing the given polynomial by w+3 </SPAN>\n" );
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