document.write( "Question 547158: what is the answer for the equation f(x)=x^4-6x^3+11x^2+12x-26 divided by 3-2i \n" ); document.write( "
Algebra.Com's Answer #356265 by Edwin McCravy(20064)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "f(x)=x^4-6x^3+11x^2+12x-26 divided by 3-2i\r\n" );
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document.write( "   3-2i |  1    -6    11    12    -26\r\n" );
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document.write( "Bring down the 1\r\n" );
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document.write( "   3-2i |  1    -6      11    12    -26\r\n" );
document.write( "        |                              \r\n" );
document.write( "           1\r\n" );
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document.write( "Multiply the 1 by the 3-2i: 1(3-2i) = 3-2i.  Write that under the -6\r\n" );
document.write( "like this:\r\n" );
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document.write( "   3-2i |  1    -6      11    12    -26\r\n" );
document.write( "        |        3-2i                  \r\n" );
document.write( "           1\r\n" );
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document.write( "Add -6 and 3-2i, getting -3-2i.  Put that underneath the line to\r\n" );
document.write( "the right of the 1, like this:\r\n" );
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document.write( "   3-2i |  1    -6      11    12    -26\r\n" );
document.write( "        |        3-2i                  \r\n" );
document.write( "           1    -3-2i\r\n" );
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document.write( "Multiply the -3-2i by the 3-2i: (-3-2i)(3-2i) = -9+6i-6i+4i² \r\n" );
document.write( "= -9+4(-1) = -9-4 = -13.  Write than under the 11 like this:\r\n" );
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document.write( "   3-2i |  1    -6      11    12    -26\r\n" );
document.write( "        |        3-2i  -13             \r\n" );
document.write( "           1    -3-2i\r\n" );
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document.write( "Add 11 and -13, getting -2.  Put that underneath the line to\r\n" );
document.write( "the right of the -3-2i, like this:\r\n" );
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document.write( "   3-2i |  1    -6      11    12    -26\r\n" );
document.write( "        |        3-2i  -13             \r\n" );
document.write( "           1    -3-2i   -2\r\n" );
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document.write( "Multiply the -2 by the 3-2i: -2(3-2i) =-6+4i.  Write that under the 12\r\n" );
document.write( "like this:\r\n" );
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document.write( "   3-2i |  1    -6      11    12     -26\r\n" );
document.write( "        |        3-2i  -13    -6+4i     \r\n" );
document.write( "           1    -3-2i   -2     6+4i\r\n" );
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document.write( "Multiply the 6+4i by the 3-2i: (6+4i)(3-2i) = 18-12i+12i-8i² \r\n" );
document.write( "= 18-8(-1) = 18+8 = 26.  Write than under the -26 like this:\r\n" );
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document.write( "   3-2i |  1    -6      11    12     -26\r\n" );
document.write( "        |        3-2i  -13    -6+4i   26\r\n" );
document.write( "           1    -3-2i   -2     6+4i\r\n" );
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document.write( "Add and get 0 remainder\r\n" );
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document.write( "   3-2i |  1    -6      11    12     -26\r\n" );
document.write( "        |        3-2i  -13    -6+4i   26\r\n" );
document.write( "           1    -3-2i   -2     6+4i    0\r\n" );
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document.write( "We interpret that bottom line as coefficients of a\r\n" );
document.write( "polynomial of one less degree than the original.  The\r\n" );
document.write( "degree of the original is 4, so this will be of degree 3:\r\n" );
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document.write( "   x³ + (-3-2i)x² - 2x + (6+4i)\r\n" );
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document.write( "That's the answer. or you can factor out a negative\r\n" );
document.write( "from the second coefficiens:\r\n" );
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document.write( "   x³ - (3+2i)x² - 2x + (6+4i)\r\n" );
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document.write( "Edwin
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