document.write( "Question 607144: how do i solve by factoring 2x2-5x-12=0 ? \n" ); document.write( "
Algebra.Com's Answer #382436 by Edwin McCravy(20056)\"\" \"About 
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document.write( "2x²-5x-12 = 0\r\n" );
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document.write( "We must factor the left side:\r\n" );
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document.write( "Multiply the 2 by the 12 ignoring signs.  Get 24\r\n" );
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document.write( "Write down all the ways to have two positive integers\r\n" );
document.write( "which have product 24, starting with 24*1\r\n" );
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document.write( "24*1\r\n" );
document.write( "12*2\r\n" );
document.write( " 8*3\r\n" );
document.write( " 6*4\r\n" );
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document.write( "Since the last sign in 2x²-5x-12 is -, SUBTRACT them,\r\n" );
document.write( "and place the DIFFERENCE out beside that:\r\n" );
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document.write( "24*1   24-1=23\r\n" );
document.write( "12*2   12-2=10\r\n" );
document.write( " 8*3    8-3=5\r\n" );
document.write( " 6*4    6-4=2\r\n" );
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document.write( "Now, again ignoring signs, we find in that list of\r\n" );
document.write( "differences the coefficient of the middle term in 2x²-5x-12\r\n" );
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document.write( "So we replace the number 5 by 8-3\r\n" );
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document.write( "2x²-5x-3 = 0\r\n" );
document.write( "2x²-(8-3)x-12 = 0\r\n" );
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document.write( "Then we distribute to remove the parentheses:\r\n" );
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document.write( "2x²-8x+3x-12 = 0\r\n" );
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document.write( "Factor the first two terms 2x²-8 by taking out the\r\n" );
document.write( "greatest common factor, 2x, getting 2x(x-4)\r\n" );
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document.write( "Factor the last two terms +3x-12 by taking out the\r\n" );
document.write( "greatest common factor, getting +3(x-4)\r\n" );
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document.write( "So we have\r\n" );
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document.write( "2x(x-4)+3(x-4) = 0\r\n" );
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document.write( "Notice that there is a common factor, (x-4)\r\n" );
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document.write( "2x(x-4)+3(x-4) = 0\r\n" );
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document.write( "which we can factor out leaving the 2x and the +3 to put \r\n" );
document.write( "in parentheses:\r\n" );
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document.write( "(x-4)(2x+3) = 0\r\n" );
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document.write( "Now we use the zero-factor property:\r\n" );
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document.write( "x-4 = 0,  2x+3 = 0\r\n" );
document.write( "  x = 4,    2x = -3\r\n" );
document.write( "             x = \"-3%2F2\"\r\n" );
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document.write( "---------------------------\r\n" );
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document.write( "Here's another example where the last term is + :\r\n" );
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document.write( "12x²-32x+21 = 0\r\n" );
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document.write( "Multiply the 12 by the 21 ignoring signs.  Get 252\r\n" );
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document.write( "Write down all the ways to have two positive integers\r\n" );
document.write( "which have product 252, starting with 252*1\r\n" );
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document.write( "252*1\r\n" );
document.write( "126*2\r\n" );
document.write( " 84*3\r\n" );
document.write( " 63*4\r\n" );
document.write( " 42*6\r\n" );
document.write( " 36*7\r\n" );
document.write( " 28*9\r\n" );
document.write( " 21*12\r\n" );
document.write( " 18*14\r\n" );
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document.write( "Since the last sign in 12x²-32x+21 is +, ADD them,\r\n" );
document.write( "and place the SUM out beside that:\r\n" );
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document.write( "252*1    252+1=253\r\n" );
document.write( "126*2    126+2=128\r\n" );
document.write( " 84*3     84+3-87\r\n" );
document.write( " 63*4     63+4=67\r\n" );
document.write( " 42*6     42+6=48\r\n" );
document.write( " 36*7     36+7=43\r\n" );
document.write( " 28*9     28+9=37 \r\n" );
document.write( " 21*12   21+12=33\r\n" );
document.write( " 18*14   18+14=32\r\n" );
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document.write( "Now, again ignoring signs, we find in that list of\r\n" );
document.write( "sums the coefficient of the middle term in 12x²-32x+21\r\n" );
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document.write( "So we replace the number 32 by 18+14\r\n" );
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document.write( "12x²-32x+21 = 0\r\n" );
document.write( "12x²-(18+14)x+21 = 0\r\n" );
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document.write( "Then we distribute to remove the parentheses:\r\n" );
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document.write( "12x²-18x-14x+21 = 0\r\n" );
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document.write( "Factor the first two terms 12x²-18x by taking out the\r\n" );
document.write( "greatest common factor, getting 6x(2x-3)\r\n" );
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document.write( "Factor the last two terms -14x+21 by taking out the\r\n" );
document.write( "greatest common factor, -7, getting -7(2x-3)\r\n" );
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document.write( "So we have\r\n" );
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document.write( "6x(2x-3)-7(2x-3) = 0\r\n" );
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document.write( "Notice that there is a common factor, (2x-3)\r\n" );
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document.write( "6x(2x-3)-7(2x-3) = 0\r\n" );
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document.write( "which we can factor out leaving the 6x and the -7 to put \r\n" );
document.write( "in parentheses:\r\n" );
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document.write( "(2x-3)(6x-7) = 0\r\n" );
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document.write( "Using the zero factor property:\r\n" );
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document.write( "    2x-3 = 0          6x-7 = 0\r\n" );
document.write( "      2x = 3            6x = 7  \r\n" );
document.write( "       x = \"3%2F2\"             x = \"7%2F6\"\r\n" );
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document.write( "Edwin
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