document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=29647>Question 29647</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When a polynomial P(x) is divided by x-1, the remainder is 5. When P(x) is divided by x-2, the remainder is 2. Find the Remainder when P(x) is divided by (x-1)(x-2).\r<BR>\n" );
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document.write( "THANKS...PLEASE ANSWER THIS!<BR>\n" );
document.write( "-Rebecca </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #16599 by </B><A HREF=/tutors/aboutme.mpl?userid=ikdeep><B>ikdeep(226)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikdeep><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=ikdeep><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=16599\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We have formula i.e.\r<BR>\n" );
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document.write( "Divident = divisor * quotient + remainder\r<BR>\n" );
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document.write( "Now according to first condition i.e. When a polynomial P(x) is divided by x-1, the remainder is 5...we get the equation....\r<BR>\n" );
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document.write( "divident i.e p(x) = (x-1)* quotient + 5\r<BR>\n" );
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document.write( "let the quotient = q\r<BR>\n" );
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document.write( "so ...divident = (x-1)* q + 5\r<BR>\n" );
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document.write( "divident = qx - 1q + 5....(1)\r<BR>\n" );
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document.write( " Now according to second condition i.e. When P(x) is divided by x-2, the remainder is 2...we get the equation....\r<BR>\n" );
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document.write( "divident i.e p(x) = (x-2)* quotient + 2\r<BR>\n" );
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document.write( "again on solving this equation we get ....\r<BR>\n" );
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document.write( "divident = qx - 2q + 2....(1).....\r<BR>\n" );
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document.write( "Also we know that divident or p(x) is same in both equation,,so we get...\r<BR>\n" );
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document.write( "qx - 2q + 2 = qx - q1 + 5\r<BR>\n" );
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document.write( " - 2q + 2 = - q1 + 5  (qx on both side wolud be eliminated).\r<BR>\n" );
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document.write( " -2q + 1q = 5 - 2\r<BR>\n" );
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document.write( "       -q = 3\r<BR>\n" );
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document.write( "or      q = -3\r<BR>\n" );
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document.write( "therefore we get the value of quotient = -3 ...\r<BR>\n" );
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document.write( "now on substituting the value of q either in (1) or (2), would give the value of divident or p(x)...and we get \r<BR>\n" );
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document.write( "divident = qx - 1q + 5....(1)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "         = -3x - (-3) + 5 \r<BR>\n" );
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document.write( "         = -3x + 3 + 5\r<BR>\n" );
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document.write( "         = -3x + 8....p(x)...\r<BR>\n" );
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document.write( "Here comes the solution of half of your question..\r<BR>\n" );
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document.write( "Now, when we see the 2nd half of the question, where you have written \"Find the Remainder when P(x) is divided by (x-1)(x-2).\"\r<BR>\n" );
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document.write( "I think that this is an incorrect statement as if you see carefully you might notice that here divident or P(x) i.e -3x + 8  (which we calculated above) is smaller than (x-1)(x-2) and such a division  will not give a logical answer .\r<BR>\n" );
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document.write( "Instead, of this, I think (x-1)(x-2) is to be divided by P(x)...\r<BR>\n" );
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document.write( "so, check the question and contact me again ...\r<BR>\n" );
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document.write( "hope this will help you \r<BR>\n" );
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document.write( "Please feel free to revert back for any further queries. </SPAN>\n" );
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