document.write( "Question 490700: I started factoring x^4-3x^3-21x^2+43x+60, but I got stuck after I synthetically divided by -1 first, now I am x^3-4x^2-17x+60. I divided by 1 and -1 and it's not working. Help! Thank you! \n" ); document.write( "
Algebra.Com's Answer #334306 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
x⁴- 3x³ - 21x² + 43x + 60
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document.write( "Possible zeros are ± the factors of 60:\r\n" );
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document.write( "±1, ±2, ±3, ±4, ±5, ±6, ±10, ±12, ±15, ±20, ±30, ±60\r\n" );
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document.write( "It's a matter of trial and error: \r\n" );
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document.write( "try -1\r\n" );
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document.write( "-1| 1 -3 -21  43  60\r\n" );
document.write( "  |   -1   4  17 -60\r\n" );
document.write( "    1 -4 -17  60   0\r\n" );
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document.write( "Yes 1 is a zero. So the factorization so far is\r\n" );
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document.write( "(x-1)(x³-4x²-17x+60)\r\n" );
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document.write( "The possible zeros of x³-4x²-17x+60 are still\r\n" );
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document.write( "±1, ±2, ±3, ±4, ±5, ±6, ±10, ±12, ±15, ±20, ±30, ±60\r\n" );
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document.write( "try 1\r\n" );
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document.write( " 1| 1 -4 -17  60\r\n" );
document.write( "  |    1  -3 -20\r\n" );
document.write( "    1 -3 -20  40\r\n" );
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document.write( "1 is not a zero of x³-4x²-17x+60\r\n" );
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document.write( "try -1\r\n" );
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document.write( "-1| 1 -4 -17  60\r\n" );
document.write( "  |   -1   5  12\r\n" );
document.write( "    1 -5 -12  72\r\n" );
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document.write( "-1 is not a zero of x³-4x²-17x+60\r\n" );
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document.write( "try 2\r\n" );
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document.write( " 2| 1 -4 -17  60\r\n" );
document.write( "  |    2  -4 -42\r\n" );
document.write( "    1 -2 -21  18\r\n" );
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document.write( "2 is not a zero of x³-4x²-17x+60\r\n" );
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document.write( "try -2\r\n" );
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document.write( "-2| 1 -4 -17  60\r\n" );
document.write( "  |   -2  12  10\r\n" );
document.write( "    1 -6  -5  70\r\n" );
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document.write( "-2 is not a zero of x³-4x²-17x+60\r\n" );
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document.write( "try 3\r\n" );
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document.write( " 3| 1 -4 -17  60\r\n" );
document.write( "  |    3  -3 -60\r\n" );
document.write( "    1 -1 -20   0\r\n" );
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document.write( "Yes 3 is a zero of x³-4x²-17x+60. So the factorization so far is\r\n" );
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document.write( "(x-1)(x-3)(x²-x-20)\r\n" );
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document.write( "We can factor the trinomial in the last parentheses without\r\n" );
document.write( "using synthetix division:\r\n" );
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document.write( "(x-1)(x-3)(x-5)(x+4)\r\n" );
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document.write( "That's the final factorization:\r\n" );
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document.write( "The zeros are 1,3,5,-4.\r\n" );
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document.write( "Edwin
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