document.write( "Question 249231: how do you factor x^2-9x+20
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Algebra.Com's Answer #181564 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
how do you factor \r
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document.write( "We try to factor it.\r\n" );
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document.write( "There is a 1 in front of the \"x%5E2\" and a POSITIVE\r\n" );
document.write( "number on the right.\r\n" );
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document.write( "\"1x%5E2-9x%2B20\"\r\n" );
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document.write( "Multiply the 1 by the 20, get 20.  Write down all the ways\r\n" );
document.write( "you can multiply two positive integers together to get 20.\r\n" );
document.write( "They are\r\n" );
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document.write( "1x20\r\n" );
document.write( "2x10\r\n" );
document.write( "4x5\r\n" );
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document.write( "Now since the last sign before the 20 is +, out to the\r\n" );
document.write( "right of those we ADD those pairs of positive integers:\r\n" );
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document.write( "1x20   20+1=21\r\n" );
document.write( "2x10   10+2=12\r\n" );
document.write( "4x5     4+5=9\r\n" );
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document.write( "Ignoring signs we see that 9 is the coefficient of the\r\n" );
document.write( "middle term, and that corresponds to factors 4 and 5,\r\n" );
document.write( "So we must put signs, either + or -, in front of 4x and 5x \r\n" );
document.write( "so they will combine to give the middle term, -9x.  We \r\n" );
document.write( "can do that by assigning a negative sign to 4x and a \r\n" );
document.write( "negative sign to 5x.  So the middle term -9x can be\r\n" );
document.write( "written as -4x-5x\r\n" );
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document.write( "So\r\n" );
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document.write( "\"x%5E2-9x%2B20\"\r\n" );
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document.write( "becomes\r\n" );
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document.write( "\"x%5E2-4x-5x%2B20\"\r\n" );
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document.write( "Factor only the first two terms:\r\n" );
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document.write( "\"x%28x-4%29-5x%2B20\"\r\n" );
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document.write( "Factor the last two terms:\r\n" );
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document.write( "\"x%28x-4%29-5%28x-4%29\"\r\n" );
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document.write( "Now notice there is a common binomial factor of\r\n" );
document.write( "\"%28x-4%29\", so we can take it out:\r\n" );
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document.write( "\"%28x-4%29%28x-5%29\"\r\n" );
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document.write( "2x^2+x-2=0\r\n" );
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document.write( "We first try to factor the left side.\r\n" );
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document.write( "There is a 1 in front of the \"x\" and a NEGATIVE\r\n" );
document.write( "number on the right.\r\n" );
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document.write( "\"2x%5E2%2B1x-2=0\"\r\n" );
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document.write( "Multiply the 2 by the 2, get 4.  Write down all the ways\r\n" );
document.write( "you can multiply two positive integers together to get 4.\r\n" );
document.write( "They are\r\n" );
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document.write( "1x4\r\n" );
document.write( "2x2\r\n" );
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document.write( "Now since the last sign before the second 2 is -, out to the\r\n" );
document.write( "right of those we SUBTRACT those pairs of positive integers:\r\n" );
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document.write( "1x4   4-1=3\r\n" );
document.write( "2x2   2-2=0\r\n" );
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document.write( "We see that the coefficient of the middle term, 1, ignoring\r\n" );
document.write( "signs, is neither 3 nor 0.  That means the trinomial will not \r\n" );
document.write( "factor.  \r\n" );
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document.write( "So we must use the quadratic formula:\r\n" );
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document.write( "\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"\r\n" );
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document.write( "with \"a=2\", \"b=1\",  \"c=-2\"\r\n" );
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document.write( "\"x+=+%28-%281%29+%2B-+sqrt%28%281%29%5E2-4%2A%282%29%2A%28-2%29%29%29%2F%282%2A%282%29%29+\"\r\n" );
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document.write( "\"x+=+%28-1+%2B-+sqrt%281%2B16%29%29%2F4+\"\r\n" );
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document.write( "\"x+=+%28-1+%2B-+sqrt%2817%29%29%2F4+\"\r\n" );
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document.write( "Edwin
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