document.write( "Question 72094: find all roots of the polynomial x3 - x2 +16x -16\r
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\n" ); document.write( "\n" ); document.write( "what does the i come from? please explain equation and solution.Thank you \n" ); document.write( "
Algebra.Com's Answer #51528 by rmromero(383)\"\" \"About 
You can put this solution on YOUR website!

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document.write( "find all roots of the polynomial x^3 - x^2 +16x -16\r
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document.write( "possible answers:
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document.write( "1, 4, -4
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document.write( "-1, 4, -4
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document.write( "-1, 4i, -4i
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document.write( "1, 4i, -4i\r
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document.write( "what does the i come from? please explain equation and solution.Thank you\r
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document.write( "To solve for the roots of the polynomial(sometimes called zeros of the polynomial)
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document.write( "Let us find possible factors of x^3 - x^2 +16x -16, p/q
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document.write( "                                 |               |
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document.write( "                                 q               p
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document.write( " Where p = 16 (possible factor) = 1, -1, 4, -4, 16, -16
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document.write( "       q = 1  (possible factor) = 1, -1\r
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document.write( "The possible factors of x^3 - x^2 +16x -16 are
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document.write( " p/q = 1, -1, 4, -4, 16, -16\r
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document.write( "Now we can use synthetic division to check which are the true factor.
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document.write( "   factor        Coefficients
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document.write( "1|            1  -1  16  -16
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document.write( "                 1   0   16
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document.write( "            _______________ 
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document.write( "             1   0  16   0 --> since no reminder, 1 is a factor of f(x)\r
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document.write( "Then lets find other factors aside from x - 1
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document.write( "             the quotient 1  0 16 means x^2 + 16 \r
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document.write( "Solve for x to find other factors of  x^3 - x^2 +16x -16:\r
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document.write( "   x^2 + 16 = 0
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document.write( "        \"sqrt%28x%5E2%29+=+sqrt%28-16%29\"
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document.write( "          \"x=+sqrt%28%2816%29%2A%28-1%29%29\" Remember \"sqrt%28-1%29+=+1\"
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document.write( "             x = ±4i\r
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document.write( "       
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document.write( "Therefore the roots of the polynomial are
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document.write( "1, 4i, -4i\r
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