document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=375366>Question 375366</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose a polynomial P(x) when divided by x-9 has a quotient of 4x^3+5x^2+7x+13 and a remainder of 88. Find P(9). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #266944 by </B><A HREF=/tutors/aboutme.mpl?userid=CharlesG2><B>CharlesG2(834)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CharlesG2><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=266944\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Suppose a polynomial P(x) when divided by x-9 has a quotient of 4x^3+5x^2+7x+13 and a remainder of 88. Find P(9).\r<BR>\n" );
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document.write( "quotient: 4x^3 + 5x^2 + 7x + 13<BR>\n" );
document.write( "quotient -> how many times did x - 9 go into P(x)<BR>\n" );
document.write( "divisor: x - 9<BR>\n" );
document.write( "remainder: 88<BR>\n" );
document.write( "dividend: P(x)\r<BR>\n" );
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document.write( "(x - 9)(4x^3 + 5x^2 + 7x + 13)<BR>\n" );
document.write( "4x^4 + 5x^3 + 7x^2 + 13x - 36x^3 - 45x^2 - 63x - 117<BR>\n" );
document.write( "4x^4 - 31x^3 - 38x^2 - 50x - 117\r<BR>\n" );
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document.write( "-117 + 88 = -29\r<BR>\n" );
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document.write( "check:<BR>\n" );
document.write( "...........4x^3 + 5x^2 + 7x + 13<BR>\n" );
document.write( "x - 9 --> 4x^4 - 31x^3 - 38x^2 - 50x - 29<BR>\n" );
document.write( "..........4x^4 - 36x^3<BR>\n" );
document.write( "..................5x^3 - 38x^2<BR>\n" );
document.write( "..................5x^3 - 45x^2<BR>\n" );
document.write( "..........................7x^2 - 50x<BR>\n" );
document.write( "..........................7x^2 - 63x<BR>\n" );
document.write( ".................................13x - 29<BR>\n" );
document.write( ".................................13x - 117<BR>\n" );
document.write( ".......................................88<BR>\n" );
document.write( "P(x) = 4x^4 - 31x^3 - 38x^2 - 50x - 29<BR>\n" );
document.write( "P(9) = 4 * 9^4 - 31 * 9^3 - 38 * 9^2 - 50 * 9 - 29<BR>\n" );
document.write( "P(9) = 4 * 6561 - 31 * 729 - 38 * 81 - 450 - 29<BR>\n" );
document.write( "P(9) = 26244 - 22599 - 3078 - 479<BR>\n" );
document.write( "P(9) = 88\r<BR>\n" );
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document.write( " </SPAN>\n" );
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