document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=536558>Question 536558</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the Remainder Theorem and Synthetic Division to find the remainders in the following division problems.\r<BR>\n" );
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document.write( "x3 - 2x2 + 5x - 6 divided by x - 3\r<BR>\n" );
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document.write( "-2x4 - 6x2 + 3x + 1 divided by x + 1\r<BR>\n" );
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document.write( "x5 + 2x4 - 3x + 3 divided by x - 1\r<BR>\n" );
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document.write( "Find a polynomial of degree three that when divided by x - 2 has a remainder of 3. You will really have to think on this one. Hint: Work backwards! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #352440 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=352440\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "There exists an infinite number of polynomial functions of degree 3 that are evenly divisible by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ -\ 2\">.  Just select your own values for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \alpha\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \beta\">, and then multiply the three binomials <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (x\ -\ \alpha)(x\ -\ \beta)(x\ -\ 2)\">.  Once you have your polynomial that IS divisible by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ -\ 2\">, add <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 3\"> to it to get a polynomial that has a remainder of 3 when divided by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ -\ 2\">.  Hint: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large P(x)\ =\ (x\ -\ 2)^3\ +\ 3\"> will work out nicely. \r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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