document.write( "Question 40421: 
Factor\r\n" );
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document.write( "x4 - x3 - 7x2 + x + 6 = 0\r\n" );
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document.write( "Possible answers:\r\n" );
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document.write( "a. (x-6)\r\n" );
document.write( "b. (x-3)\r\n" );
document.write( "c. (x-2)\r\n" );
document.write( "d. (x+6)
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Algebra.Com's Answer #25785 by AnlytcPhil(1807)\"\" \"About 
You can put this solution on YOUR website!
Factor\r\n" );
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document.write( "x4 - x3 - 7x2 + x + 6 = 0\r\n" );
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document.write( "Possible answers:\r\n" );
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document.write( "a. (x-6)\r\n" );
document.write( "b. (x-3)\r\n" );
document.write( "c. (x-2)\r\n" );
document.write( "d. (x+6)\r\n" );
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document.write( "x4 - x3 - 7x2 + x + 6 = 0\r\n" );
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document.write( "We divide x4 - x3 - 7x2 + x + 6 \r\n" );
document.write( "synthetically by each of those to find out which one gives a zero\r\n" );
document.write( "remainder. I already know which one it is, so I'll try all the \r\n" );
document.write( "others first so you'll get the idea.\r\n" );
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document.write( "Let's try dividing x4 - x3 - 7x2 + x + 6\r\n" );
document.write( "synthetically by (x-6). Change the sign of -6 to 6 for \r\n" );
document.write( "synthetic division:\r\n" );
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document.write( "  6 | 1  -1  -7   1   6\r\n" );
document.write( "    |     6  30 138 834\r\n" );
document.write( "      1   5  23 139 840\r\n" );
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document.write( "No,  840 is not 0, so\r\n" );
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document.write( "Let's try dividing x4 - x3 - 7x2 + x + 6\r\n" );
document.write( "synthetically by (x-2). Change the sign of -2 to 2 for \r\n" );
document.write( "synthetic division:\r\n" );
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document.write( "  2 | 1  -1  -7   1   6\r\n" );
document.write( "    |     2   2 -10 -18 \r\n" );
document.write( "      1   1  -5  -9 -12\r\n" );
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document.write( "No, -12 is not 0, so\r\n" );
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document.write( "Let's try dividing x4 - x3 - 7x2 + x + 6\r\n" );
document.write( "synthetically by (x+6). Change the sign of +2 to -6 for \r\n" );
document.write( "synthetic division:\r\n" );
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document.write( " -6 | 1  -1  -7    1     6\r\n" );
document.write( "    |    -6  42 -210  1254 \r\n" );
document.write( "      1  -7  35 -209  1260\r\n" );
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document.write( "No, 1260 is not 0, so\r\n" );
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document.write( "Let's try dividing x4 - x3 - 7x2 + x + 6\r\n" );
document.write( "synthetically by (x-3). Change the sign of -3 to 3 for \r\n" );
document.write( "synthetic division:\r\n" );
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document.write( "  3 | 1  -1  -7   1   6\r\n" );
document.write( "    |     3   6  -3  -6 \r\n" );
document.write( "      1   2  -1  -2   0\r\n" );
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document.write( "Yes!!!! That remainder is 0.  So the quotient is gotten from the\r\n" );
document.write( "other numbers on the bottom, 1  2 -1 -2, which means \r\n" );
document.write( "1x3 + 2x2 - 1x - 2.  So we have factored x4 - x3 - 7x2 + x + 6 as\r\n" );
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document.write( "(x - 3)(x3 + 2x2 - x - 2) = 0\r\n" );
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document.write( "Now we can factor the x3 + 2x2 - x - 2 by grouping\r\n" );
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document.write( "x3 + 2x2 - x - 2\r\n" );
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document.write( "Factor x2 out of the first two terms and -1 out of the \r\n" );
document.write( "last two terms:\r\n" );
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document.write( "x2(x + 2) - 1(x + 2)\r\n" );
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document.write( "Then factor out (x + 2) and get\r\n" );
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document.write( "(x + 2)(x2 - 1)\r\n" );
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document.write( "Then factor the (x2 - 1) as (x - 1)(x + 1)\r\n" );
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document.write( "So the polynomial equation\r\n" );
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document.write( "x4 - x3 - 7x2 + x + 6 = 0\r\n" );
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document.write( "is now factored completely as\r\n" );
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document.write( "(x - 3)(x + 2)(x - 1)(x + 1) = 0\r\n" );
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document.write( "That's what you were told to do.  However they only gave you \r\n" );
document.write( "one of the factors so to get the problem right all you had to \r\n" );
document.write( "do was the first part and get (b).\r\n" );
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document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com
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