document.write( "Question 827794: Factor the following polynomials x2+12x-28 \n" ); document.write( "
Algebra.Com's Answer #498910 by AnlytcPhil(1806) $\"\"$ $\"About$
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document.write( "Factor x²+12x-28\r\n" );
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document.write( "Write this\r\n" );
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document.write( "Think of two POSITIVE whole numbers which multiply to give this\r\n" );
document.write( "number, 28,........\r\n" );
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document.write( "........which subtract (because of this sign)....,\r\n" );
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document.write( ".......to give this POSITIVE number, 12,.......\r\n" );
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document.write( "So the only two POSITIVE integers that multiply\r\n" );
document.write( "to give 28 and subtract to give 12, are 14 and 2,\r\n" );
document.write( "because 14 times 2 is 28 and 14 minus 2 is 12.\r\n" );
document.write( "So we put 14 and 2 in the parentheses like this:\r\n" );
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document.write( "(x 14)(x 2)\r\n" );
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document.write( "All we need do is put the correct signs in the \r\n" );
document.write( "middle of each parentheses.\r\n" );
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document.write( "The larger of these two numbers (which is 14 in this case)....\r\n" );
document.write( "will always get this sign (which is +):\r\n" );
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document.write( "So we put a \"+\" sign before the 14 in the\r\n" );
document.write( "first parentheses:\r\n" );
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document.write( "(x+14)(x 2)\r\n" );
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document.write( "Now we need to decide what sign goes in the\r\n" );
document.write( "middle of the second parentheses:\r\n" );
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document.write( "We look back at this sign:\r\n" );
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document.write( "Since it is a \"-\" the second parentheses gets\r\n" );
document.write( "the OPPOSITE sign from the sign in the other\r\n" );
document.write( "parentheses (so it gets a - ):\r\n" );
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document.write( "(x+14)(x-2)\r\n" );
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document.write( "That's the answer.\r\n" );
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document.write( "Let's do another problem like that:\r\n" );
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document.write( "x²-9x+14\r\n" );
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document.write( "Write this\r\n" );
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document.write( "(x  )(x  )\r\n" );
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document.write( "Think of two POSITIVE whole numbers which multiply to give this\r\n" );
document.write( "number, 14,........\r\n" );
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document.write( "........that add (because of this + sign)....,\r\n" );
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document.write( ".......to give this POSITIVE number, 9,.......\r\n" );
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document.write( "So the only two POSITIVE integers that multiply\r\n" );
document.write( "to give 14 and add to give 9, are 7 and 2,\r\n" );
document.write( "because 7 times 2 is 14 and 7 plus 2 is 9.\r\n" );
document.write( "So we put 7 and 2 in the parentheses like this:\r\n" );
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document.write( "(x 7)(x 2)\r\n" );
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document.write( "All we need do is put the correct signs in the \r\n" );
document.write( "middle of each parentheses.\r\n" );
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document.write( "The larger of these two numbers (which is 7 in this case)....\r\n" );
document.write( "will always get this sign (which is -):\r\n" );
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document.write( "So we put a \"-\" sign before the 7 in the\r\n" );
document.write( "first parentheses:\r\n" );
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document.write( "(x-7)(x 2)\r\n" );
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document.write( "Now we need to decide what sign goes in the\r\n" );
document.write( "middle of the second parentheses:\r\n" );
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document.write( "We look back at this sign:\r\n" );
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document.write( "Since it is a \"+\" the second parentheses gets\r\n" );
document.write( "the SAME sign as the sign in the other\r\n" );
document.write( "parentheses (so it also gets a - ):\r\n" );
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document.write( "(x-7)(x-2)\r\n" );
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document.write( "That's the answer.\r\n" );
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document.write( "Edwin

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