document.write( "Question 210907: If P(x)=3x^3+2x^2+x+20 and we write P(x) in the form P(x)=A+B(x-1)+C(x-1) (x-2)+D(x-1)(x-2)(x-3) A=? and B=? \n" ); document.write( "
Algebra.Com's Answer #159481 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
If P(x)=3x^3+2x^2+x+20 and we write \r
\n" ); document.write( "\n" ); document.write( "P(x) in the form P(x)=A+B(x-1)+C(x-1) (x-2)+D(x-1)(x-2)(x-3) A=? and B=?\r
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "Set both expressions for P(x) equal to each other:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Choose values for x that will cause some of those expresions\r\n" );
document.write( "in parentheses to become 0.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Substitute 1 for x in the above:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\"3%2B2%2B1%2B20+=+A%2BB%280%29%2BC%280%29%28-1%29%2BD%280%29%28-1%29%28-2%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"26+=A\"\r\n" );
document.write( "\r\n" );
document.write( "---\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now substitute 2 for x in the above:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\"24%2B8%2B2%2B20+=+A%2BB\"\r\n" );
document.write( "\r\n" );
document.write( "\"54=A%2BB\"\r\n" );
document.write( "\r\n" );
document.write( "And since A=26, substituting:\r\n" );
document.write( "\r\n" );
document.write( "\"54=A%2BB\"\r\n" );
document.write( "\r\n" );
document.write( "\"54=26%2BB\"\r\n" );
document.write( "\r\n" );
document.write( "\"28=B\"\r\n" );
document.write( "\r\n" );
document.write( "So \"A=2\" and \"B=28\"\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );