document.write( "Question 360498: Can someone factor this please?\r
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Algebra.Com's Answer #257207 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "36x² - 97x + 36\r\n" );
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document.write( "Multiply the 36 by 36, disregarding signs, getting 1296.\r\n" );
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document.write( "Write down a list of all the ways to factor 1296 using two \r\n" );
document.write( "positive integers:\r\n" );
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document.write( "1296*1\r\n" );
document.write( " 648*2\r\n" );
document.write( " 432*3\r\n" );
document.write( " 324*4\r\n" );
document.write( " 216*6\r\n" );
document.write( " 162*8\r\n" );
document.write( " 144*9\r\n" );
document.write( " 108*12\r\n" );
document.write( "  81*16\r\n" );
document.write( "  72*18\r\n" );
document.write( "  54*24\r\n" );
document.write( "  48*27\r\n" );
document.write( "  36*36\r\n" );
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document.write( "Now look at the sign of the last term to see whether we add or\r\n" );
document.write( "subtract those pairs of numbers.  The last term is +36, which\r\n" );
document.write( "has a + sign, so we add those same pairs of numbers that\r\n" );
document.write( "we multiplied above to get 1296. \r\n" );
document.write( "(when the last term has a - sign, we subtract, but since it has a +, we add):\r\n" );
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document.write( "1296+1  = 1297\r\n" );
document.write( " 648+2  =  650\r\n" );
document.write( " 432+3  =  435 \r\n" );
document.write( " 324+4  =  328\r\n" );
document.write( " 216+6  =  222\r\n" );
document.write( " 162+8  =  170\r\n" );
document.write( " 144+9  =  243\r\n" );
document.write( " 108+12 =  120\r\n" );
document.write( "  81+16 =   97\r\n" );
document.write( "  72+18 =   90\r\n" );
document.write( "  54+24 =   78\r\n" );
document.write( "  48+27 =   75 \r\n" );
document.write( "  36+36 =   72\r\n" );
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document.write( "Next we look down that list to find the coefficient of\r\n" );
document.write( "the middle term of 36x² - 97x + 36, in absolute value,\r\n" );
document.write( "which is 97 and we find it as\r\n" );
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document.write( "  81+16 =   97\r\n" );
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document.write( "So we substitute (81+16) in place of 97\r\n" );
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document.write( "  36x² - 97x + 36\r\n" );
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document.write( "36x² - (81+16)x + 36\r\n" );
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document.write( "and remove the parentheses:\r\n" );
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document.write( "36x² - 81x - 16x + 36\r\n" );
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document.write( "Next we factor only the FIRST two terms by\r\n" );
document.write( "factoring out 9x:\r\n" );
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document.write( "9x(4x - 9) - 16x + 36\r\n" );
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document.write( "Next we factor only the LAST two terms by\r\n" );
document.write( "factoring out -4:\r\n" );
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document.write( "9x(4x - 9) - 4(4x - 9)\r\n" );
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document.write( "Notice that the two parentheses are the same.\r\n" );
document.write( "I'll color them red:\r\n" );
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document.write( "9x(4x - 9) - 4(4x - 9)\r\n" );
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document.write( "So factor out the red factor, leaving the black factors as terms in \r\n" );
document.write( "parentheses:\r\n" );
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document.write( "(4x - 9)(9x - 4)\r\n" );
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document.write( "Edwin
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