document.write( "Question 83825: I am confused about grouping.
\n" ); document.write( "x2-11x+28=0\r
\n" ); document.write( "\n" ); document.write( "I know (x- )(x+ )
\n" ); document.write( "but...which number am I trying to break down? They are not divisible. \n" ); document.write( "
Algebra.Com's Answer #60292 by Edwin McCravy(20086)\"\" \"About 
You can put this solution on YOUR website!
I am confused about grouping.\r\n" );
document.write( "x² - 11x + 28 = 0 \r\n" );
document.write( "I know (x- )(x+ )\r\n" );
document.write( "but...which number am I trying to break down? They are not divisible. \r\n" );
document.write( "\r\n" );
document.write( "--------------------------\r\n" );
document.write( "\r\n" );
document.write( "There are four cases to learn when the coefficient of x² is 1:\r\n" );
document.write( "\r\n" );
document.write( "--------------------------\r\n" );
document.write( "\r\n" );
document.write( "I. When you want to factor\r\n" );
document.write( "\r\n" );
document.write( "x² + Ax + B\r\n" );
document.write( "\r\n" );
document.write( "where A and B are positive integers\r\n" );
document.write( "\r\n" );
document.write( "1. Think of two positive integers which have product B and sum A\r\n" );
document.write( "2. If those positive integers are C and D, then factorization is\r\n" );
document.write( "   (x + C)(x + D)\r\n" );
document.write( "\r\n" );
document.write( "---------------------------\r\n" );
document.write( "\r\n" );
document.write( "II. When you want to factor\r\n" );
document.write( "\r\n" );
document.write( "x² - Ax + B\r\n" );
document.write( "\r\n" );
document.write( "where A and B are positive integers\r\n" );
document.write( "\r\n" );
document.write( "1. Think of two positive integers which have product B and sum A\r\n" );
document.write( "2. If those positive integers are C and D, then factorization is\r\n" );
document.write( "   (x - C)(x - D)\r\n" );
document.write( "\r\n" );
document.write( "----------------------------\r\n" );
document.write( "\r\n" );
document.write( "III. When you want to factor\r\n" );
document.write( "\r\n" );
document.write( "x² + Ax - B\r\n" );
document.write( "\r\n" );
document.write( "where A and B are positive integers\r\n" );
document.write( "\r\n" );
document.write( "1. Think of two positive integers which have product B and difference A\r\n" );
document.write( "2. If those positive integers are C and D, where C is the larger, then\r\n" );
document.write( "   factorization is\r\n" );
document.write( "   (x + C)(x - D)\r\n" );
document.write( "\r\n" );
document.write( "---------------------------\r\n" );
document.write( "\r\n" );
document.write( "IV. When you want to factor\r\n" );
document.write( "\r\n" );
document.write( "x² - Ax - B\r\n" );
document.write( "\r\n" );
document.write( "where A and B are positive integers\r\n" );
document.write( "\r\n" );
document.write( "1. Think of two positive integers which have product B and sum A\r\n" );
document.write( "2. If those positive integers are C and D, where C is the larger,\r\n" );
document.write( "   then factorization is\r\n" );
document.write( "   (x - C)(x + D)\r\n" );
document.write( "\r\n" );
document.write( "-----------------------------------\r\n" );
document.write( "\r\n" );
document.write( "Yours is case II.\r\n" );
document.write( "\r\n" );
document.write( "x² - 11x + 28\r\n" );
document.write( "\r\n" );
document.write( "where 11 and 28 are positive integers\r\n" );
document.write( "\r\n" );
document.write( "1. Think of two positive integers which have product 28 and sum 11\r\n" );
document.write( "2. Those positive integers are 7 and 4, thus the factorization is\r\n" );
document.write( "   (x - 7)(x - 4)\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );