document.write( "Question 1092373: Determine the value of m so that when f(x) is divided by (x-4) the remainder is -8. f(x)=3x^2+mx+4 \n" ); document.write( "
Algebra.Com's Answer #706977 by Edwin McCravy(20060) You can put this solution on YOUR website! \r\n" ); document.write( "There are two ways to do this problem.\r\n" ); document.write( "\r\n" ); document.write( "Method 1:\r\n" ); document.write( "\r\n" ); document.write( "The remainder theorem states: \r\n" ); document.write( "\r\n" ); document.write( "When a polynomial f(x) is divided by (x-r), the remainder is f(r).\r\n" ); document.write( "\r\n" ); document.write( "Therefore f(4) = -8\r\n" ); document.write( "\r\n" ); document.write( " 3(4)² + m(4) + 4 = -8\r\n" ); document.write( " 3(16) + 4m + 4 = -8\r\n" ); document.write( " 48 + 4m + 4 = -8\r\n" ); document.write( " 52 + 4m = -8\r\n" ); document.write( " 4m = -60\r\n" ); document.write( " m = -15\r\n" ); document.write( "\r\n" ); document.write( "Method 2:\r\n" ); document.write( "\r\n" ); document.write( "You can also do it by synthetic division\r\n" ); document.write( "\r\n" ); document.write( "4 | 3 m 4\r\n" ); document.write( " | 12 4(m+12)\r\n" ); document.write( " 3 m+12 4+4(m+12)\r\n" ); document.write( "\r\n" ); document.write( "Then set the remainder equal to -8\r\n" ); document.write( "\r\n" ); document.write( " 4+4(m+12) = -8\r\n" ); document.write( " 4+4m+48 = -8\r\n" ); document.write( " 52+4m = -8\r\n" ); document.write( " 4m = -60\r\n" ); document.write( " m = -15\r\n" ); document.write( "\r\n" ); document.write( "Edwin\n" ); document.write( " |