document.write( "Question 1209699: Let p(x) be a cubic polynomial. If p(0) = 0, p(1) = 1, p(2) = 2, and p(3) = 3, then compute p(4).
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #849831 by ikleyn(52781)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "Let p(x) be a cubic polynomial. If p(0) = 0, p(1) = 1, p(2) = 2, and p(3) = 3, then compute p(4).
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "        It can be solved/worded/presented differently,  in much shorter way.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "Consider the polynomial p(x) - x.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It is easy to check that the polynomial p(x)-x takes the value of 0 at the points x= 0, 1, 2, 3.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "In other words, the polynomial p(x)-x has 4 (four) different roots.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Since the polynomial P(x)-x has the degree not greater than 3, from Algebra, \r\n" );
document.write( "it implies that the polynomial is identically equal to zero.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, we proved that  p(x) - x = 0.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It implies  p(x) = x.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then p(4) = 4.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  We proved that under given condition, the polynomial p(x) is equal to x: p(x) = x, and p(4) = 4.\r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "--------------------------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Strictly speaking, the problem formulation, as it is presented in the post, is INCORRECT.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "A correct formulation should be in THIS form:\r
\n" ); document.write( "\n" ); document.write( "
 \r\n" );
document.write( "    Polynomial p(x) has a degree less than 4.  \r\n" );
document.write( "    If p(0) = 0, p(1) = 1, p(2) = 2, and p(3) = 3, then compute p(4).\r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "As it is given in the post, it demonstrates \"highlight%28highlight%28explicitly%29%29\"
\n" ); document.write( "to all people around that the problem's creator does not know basics of Algebra
\n" ); document.write( "and can not express his thoughts in mathematically correct form.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );