document.write( "Question 652540: Factor x^4-x^3+2x^2-4x-8 \n" ); document.write( "
Algebra.Com's Answer #408015 by Edwin McCravy(20060)\"\" \"About 
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document.write( "x4-x³+2x²-4x-8\r\n" );
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document.write( "The factors of 8 are 1,2,and 4, so\r\n" );
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document.write( "The possible zeros are ±1, ±2, ±4, ±8\r\n" );
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document.write( "Try 1 as a zero using synthetic division.\r\n" );
document.write( "That is we divide by x-1\r\n" );
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document.write( "1 | 1  -1   2  -4  -8\r\n" );
document.write( "  |     1   0   2  -2\r\n" );
document.write( "    1   0   2  -2 -10\r\n" );
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document.write( "No, the remainder is not a zero because it is -10, not 0.\r\n" );
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document.write( "Try -1 as a zero using synthetic division.\r\n" );
document.write( "That is, we divide by x+1\r\n" );
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document.write( "-1 | 1  -1   2  -4  -8\r\n" );
document.write( "   |    -1   2  -4   8\r\n" );
document.write( "     1  -2   4  -8   0\r\n" );
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document.write( "Yes, the remainder is 0, so that means x+1 is a factor and gives\r\n" );
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document.write( "    1x³-2x²+4x-8 as a quotient, so the original polynomial\r\n" );
document.write( "factors as\r\n" );
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document.write( "   (x+1)(x³-2x²+4x-8)\r\n" );
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document.write( "So we start over this time with x³-2x²+4x-8\r\n" );
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document.write( "The factors of 8 are 1,2,and 4, so\r\n" );
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document.write( "The possible zeros are ±1, ±2, ±4, ±8\r\n" );
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document.write( "There is no need to try 1 because it was not a factor of the original\r\n" );
document.write( "polynomial\r\n" );
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document.write( "So we try -1 as a zero using synthetic division.\r\n" );
document.write( "That is, we divide by x+1\r\n" );
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document.write( "-1 | 1  -2   4  -8\r\n" );
document.write( "   |    -1   3  -7  \r\n" );
document.write( "     1  -3   7 -15\r\n" );
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document.write( "No, the remainder is not a zero because it is -15, not 0.\r\n" );
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document.write( "Try 2 as a zero using synthetic division.\r\n" );
document.write( "That is, we divide by x-2\r\n" );
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document.write( " 2 | 1  -2   4  -8\r\n" );
document.write( "   |     2   0   8  \r\n" );
document.write( "     1   0   4   0\r\n" );
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document.write( "Yes, the remainder is 0, so that means x-2 is a factor and gives\r\n" );
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document.write( "    1x²+0x+4 as a quotient, so the original polynomial\r\n" );
document.write( "factors as\r\n" );
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document.write( "   (x+1)(x-2)(x²+4)\r\n" );
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document.write( "It doesn't factor further using real numbers.\r\n" );
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document.write( "Edwin
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