Algebra.Com's Answer #64919 by jim_thompson5910(35256)![\"\"](\"/images/stars/stars-13.gif\")  
You can put this solution on YOUR website!
In order to factor  , first multiply 5 and -6 to get -30 and we need to ask ourselves: What two numbers multiply to -30 and add to 7? Lets find out by listing all of the possible factors of -30\r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "Factors:\r
\n" );
document.write( "\n" );
document.write( "1,2,3,5,6,10,15,30,\r
\n" );
document.write( "\n" );
document.write( "-1,-2,-3,-5,-6,-10,-15,-30, List the negative factors as well. This will allow us to find all possible combinations\r
\n" );
document.write( "\n" );
document.write( "These factors pair up to multiply to -30.\r
\n" );
document.write( "\n" );
document.write( "(-1)*(30)=-30\r
\n" );
document.write( "\n" );
document.write( "(-2)*(15)=-30\r
\n" );
document.write( "\n" );
document.write( "(-3)*(10)=-30\r
\n" );
document.write( "\n" );
document.write( "(-5)*(6)=-30\r
\n" );
document.write( "\n" );
document.write( " Now which of these pairs add to 7? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 7\r
\n" );
document.write( "\n" );
document.write( "| First Number | | | Second Number | | | Sum | | 1 | | | -30 | || | 1+(-30)=-29 | | 2 | | | -15 | || | 2+(-15)=-13 | | 3 | | | -10 | || | 3+(-10)=-7 | | 5 | | | -6 | || | 5+(-6)=-1 | | -1 | | | 30 | || | (-1)+30=29 | | -2 | | | 15 | || | (-2)+15=13 | | -3 | | | 10 | || | (-3)+10=7 | | -5 | | | 6 | || | (-5)+6=1 | We can see from the table that -3 and 10 add to 7. So the two numbers that multiply to -30 and add to 7 are: -3 and 10\r
\n" );
document.write( "\n" );
document.write( " So the original quadratic\r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "\r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "breaks down to this (just replace  with the two numbers that multiply to -30 and add to 7, which are: -3 and 10)\r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "  \r
\n" );
document.write( "\n" );
document.write( "Group the first two terms together and the last two terms together like this:\r
\n" );
document.write( "\n" );
document.write( " \r
\n" );
document.write( "\n" );
document.write( "Factor a y out of the first group and factor a 2 out of the second group.\r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( " \r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "Now since we have a common term  we can combine the two terms. \r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( " Combine like terms. \r
\n" );
document.write( "\n" );
document.write( "Answer:\r
\n" );
document.write( "\n" );
document.write( "So the quadratic factors to\r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "\r
\n" );
document.write( "
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "Notice how foils back to our original problem . This verifies our answer. \n" );
document.write( " \n" );
|