document.write( "Question 160520: Use the Factor Theorem to determine whether x - c is a factor of the following function. Write in the form f ( x ) = (x - c) (quotient) if f( x ) = -4x^3 + 5x^2 + 8; c = -2 \n" ); document.write( "
Algebra.Com's Answer #118382 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!

\n" ); document.write( "Use the Factor Theorem to determine whether \"x+-+c\" is a factor of the following function. Write in the form \"f+%28+x+%29+=+%28x+-+c%29+%28quotient%29\"\r
\n" ); document.write( "\n" ); document.write( "if \"f%28+x+%29+=+-4x%5E3+%2B+5x%5E2+%2B+8\"; \"c+=+-2\"
\n" ); document.write( "
\r\n" );
document.write( "We must insert a +\"0x\"\r\n" );
document.write( "\r\n" );
document.write( "\"f%28+x+%29+=+-4x%5E3+%2B+5x%5E2+%2B+0x%2B8\" \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "-2|-4  5    0   8\r\n" );
document.write( "  |    8  -26  52\r\n" );
document.write( "   -4 13  -26  60\r\n" );
document.write( "\r\n" );
document.write( "No \"x-c\" is not a factor or the 60 remainder would have been a 0.\r\n" );
document.write( "\r\n" );
document.write( "-----------------------------------------------------------------\r\n" );
document.write( "\r\n" );
document.write( "Suppose the problem has been instead:\r\n" );
document.write( "\r\n" );
document.write( "\"f%28+x+%29+=+-4x%5E3+%2B+5x%5E2+%2B+12\"; \"c+=+2\" \r\n" );
document.write( "\r\n" );
document.write( "We must insert a +\"0x\"\r\n" );
document.write( "\r\n" );
document.write( "\"f%28+x+%29+=+-4x%5E3+%2B+5x%5E2+%2B+0x%2B12\" \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " 2|-4  5   0  12\r\n" );
document.write( "  |   -8  -6 -12\r\n" );
document.write( "   -4 -3  -6   0\r\n" );
document.write( "\r\n" );
document.write( "\"x-c\" is a factor because the remainder is 0.\r\n" );
document.write( "\r\n" );
document.write( "To write it in the form \"f+%28+x+%29+=+%28x+-+c%29+%28quotient%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"f+%28+x+%29+=+%28x+-+2%29%28-4x%5E2-3x-6%29\"\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\r
\n" ); document.write( "\n" ); document.write( " \r
\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( "
\n" );