document.write( "Question 96023: Use the ac test to determine if the following trinomial can be factored. If it can be factored, find the values of m and n.
\n" ); document.write( " 3x^2 + 11x – 4
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #69916 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!
factor \r
\n" ); document.write( "\n" ); document.write( "Use the ac test to determine if the following trinomial can be factored. If it can be factored, find the values of m and n.\r
\n" ); document.write( "\n" ); document.write( " 3x² + 11x – 4\r
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Different books and different teachers use slightly different\r\n" );
document.write( "terminology, so I'm not sure what you mean by \"m and n\".  However\r\n" );
document.write( "I'll take you through the \"ac\" method and tell you what part I \r\n" );
document.write( "think your teacher means by \"m and n\".  But you should ask to make\r\n" );
document.write( "sure.\r\n" );
document.write( "\r\n" );
document.write( "3x² + 11x - 4\r\n" );
document.write( "\r\n" );
document.write( "1. Multiply the 3 by the 4, get 12.\r\n" );
document.write( "\r\n" );
document.write( "2. Notice the sign of the last term is -, so we think \"DIFFERENCE\".\r\n" );
document.write( "(If the sign of the last term had been +, we would think \"SUM\")\r\n" );
document.write( "\r\n" );
document.write( "3. Think of two positive integers which have product 12 and\r\n" );
document.write( "DIFFERENCE 11, the coefficient (in absolute value) of the middle term.\r\n" );
document.write( "\r\n" );
document.write( "It doesn't take long to see that two such positive integers are \r\n" );
document.write( "12 and 1.  That's because 12 TIMES 1 is 12 and 12 MINUS 1 is 11.\r\n" );
document.write( "\r\n" );
document.write( "4. Now use 12 and 1 to rewrite the 11 as (12 - 1)\r\n" );
document.write( "\r\n" );
document.write( "3x² + (12 - 1)x - 4\r\n" );
document.write( "\r\n" );
document.write( "5. Remove the parentheses by distributing\r\n" );
document.write( "\r\n" );
document.write( "3x² + 12x - 1x - 4\r\n" );
document.write( "\r\n" );
document.write( "[I think your teacher calls m = 12 and n = -1, the coefficients\r\n" );
document.write( "of x above, but be sure to ask him/her.]\r\n" );
document.write( "\r\n" );
document.write( "6. Factor by grouping. That is:\r\n" );
document.write( "\r\n" );
document.write( "a. Factor the first two terms by taking\r\n" );
document.write( "out 3x.\r\n" );
document.write( "\r\n" );
document.write( "b. Factor the last two terms by taking out -1\r\n" );
document.write( "\r\n" );
document.write( "3x(x + 4) - 1(x + 4)\r\n" );
document.write( "\r\n" );
document.write( "c. Now notice that (x + 4) is contained in both expressions:\r\n" );
document.write( "\r\n" );
document.write( "3x(x + 4) - 1(x + 4)\r\n" );
document.write( "\r\n" );
document.write( "d. So factor out the whole (x + 4) leaving 3x when factoring\r\n" );
document.write( "it out of the left expression, and leaving -1 when factoring\r\n" );
document.write( "(x + 4) out on the right expression.\r\n" );
document.write( "\r\n" );
document.write( "(x + 4)(3x - 1)\r\n" );
document.write( "\r\n" );
document.write( "That's it!\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( " \n" ); document.write( "

\n" );