document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=948077>Question 948077</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Give an example of polynomials p and q of degree 3<BR>\n" );
document.write( "such that p(1) = q(1), p(2) = q(2), and p(3) = q(3),<BR>\n" );
document.write( "but p(4) is not equal to q(4). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #578659 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=578659\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given: p(x) - q(x) = 0 has roots at x = 1, 2, 3\r<BR>\n" );
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document.write( "Therefore p(x) - q(x) = C(x-1)(x-2)(x-3) for constant C.\r<BR>\n" );
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document.write( "To simplify things, let C = 1. We can pick any cubic polynomials p, q with degree 3 that satisfy the constraint. A simple example is to let\r<BR>\n" );
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document.write( "p(x) = (x-1)(x-2)(x-3) + x^3<BR>\n" );
document.write( "q(x) = x^3\r<BR>\n" );
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document.write( "Then p(i) = q(i) for i = 1,2,3, but p(4) = 70 and q(4) = 64. </SPAN>\n" );
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