document.write( "Question 288189: How do i factor \"x%5E3%2B3x%5E2-18x-40\" \n" ); document.write( "
Algebra.Com's Answer #208873 by AnlytcPhil(1806)\"\" \"About 
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How do i factor \"x%5E3%2B3x%5E2-18x-40\"
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document.write( "Since the leading coefficient is 1, if there\r\n" );
document.write( "are any rational zeros, they will all be\r\n" );
document.write( "± the integer factor of the absolute value of the\r\n" );
document.write( "numerical term -40.  So if there are any, they will\r\n" );
document.write( "be among these:\r\n" );
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document.write( "±1,±2,±4,±5,±8,±10,±20\r\n" );
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document.write( "We begin by trying +1 using synthetic division:\r\n" );
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document.write( "1 | 1  3  -18  -40\r\n" );
document.write( "  |    1    4  -14\r\n" );
document.write( "    1  4  -14  -54\r\n" );
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document.write( "So, 1 is not a zero, and so x-1 is not a factor.\r\n" );
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document.write( "We try -1:\r\n" );
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document.write( "-1 | 1  3 -18  -40\r\n" );
document.write( "   |   -1  -2   20\r\n" );
document.write( "     1  2 -20  -20\r\n" );
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document.write( "So, -1 is not a zero, and so x+1 is not a factor.\r\n" );
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document.write( "We try +2:\r\n" );
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document.write( "2 | 1  3 -18  -40\r\n" );
document.write( "  |    2  10  -16\r\n" );
document.write( "    1  5  -8  -56\r\n" );
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document.write( "So, 2 is not a zero, and so x-2 is not a factor.\r\n" );
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document.write( "We try -2:\r\n" );
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document.write( "-2 | 1  3 -18  -40\r\n" );
document.write( "   |   -2  -2   40\r\n" );
document.write( "     1  1 -20    0\r\n" );
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document.write( "Eureka!  We get a 0 remainder, so x+2 is a factor.\r\n" );
document.write( "An the numbers on the bottom row of the synthetic\r\n" );
document.write( "division left of the remainder 0 tell us the other\r\n" );
document.write( "factor.  So we have now factored\r\n" );
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document.write( "\"x%5E3%2B3x%5E2-18x-40\"\r\n" );
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document.write( "as\r\n" );
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document.write( "\"%28x%2B2%29%28x%5E2%2Bx-20%29\"\r\n" );
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document.write( "Now we can factor the trinomial in\r\n" );
document.write( "the second parentheses and we have the\r\n" );
document.write( "complete factorization as:\r\n" );
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document.write( "\"%28x%2B2%29%28x%2B5%29%28x-4%29\"\r\n" );
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document.write( "Edwin
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