document.write( "Question 421266: Use synthetic division to divide the first polynomial by the second.\r
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Algebra.Com's Answer #294204 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
Use synthetic division to divide the first polynomial by the second.
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document.write( "x³ - 2x + 1\r\n" );
document.write( "x + 4\r\n" );
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document.write( "Write the first polynomial as\r\n" );
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document.write( "x³ + 0x² - 2x + 1\r\n" );
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document.write( "Change the sign of +4 to -4\r\n" );
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document.write( "-4|1  0  -2  1\r\n" );
document.write( "  |            \r\n" );
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document.write( "Bring down the 1\r\n" );
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document.write( "-4|1  0  -2  1\r\n" );
document.write( "  |            \r\n" );
document.write( "   1\r\n" );
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document.write( "Multiply the 1 by the -4 and write it above above and to the right\r\n" );
document.write( "of the 1 that you just brought down\r\n" );
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document.write( "-4|1  0  -2  1    \r\n" );
document.write( "  |  -4        \r\n" );
document.write( "   1\r\n" );
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document.write( "Add the 0 and the -4, getting -4, and write it under the -4\r\n" );
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document.write( "-4|1  0  -2  1\r\n" );
document.write( "  |  -4        \r\n" );
document.write( "   1 -4\r\n" );
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document.write( "Multiply the -4 at the bottom by the -4 at the far left, getting 16.\r\n" );
document.write( "Write that above and to the right of the -4 at the bottom:\r\n" );
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document.write( "-4|1  0  -2  1\r\n" );
document.write( "  |  -4  16    \r\n" );
document.write( "   1 -4\r\n" );
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document.write( "Add the -2 and the 16, getting 14, and write it under the 16\r\n" );
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document.write( "-4|1  0  -2  1\r\n" );
document.write( "  |  -4  16    \r\n" );
document.write( "   1 -4  14\r\n" );
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document.write( "Multiply the 14 at the bottom by the -4 at the far left, getting -56.\r\n" );
document.write( "Write that above and to the right of the 14 at the bottom:\r\n" );
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document.write( "-4|1  0  -2   1\r\n" );
document.write( "  |  -4  16 -56\r\n" );
document.write( "   1 -4  14 \r\n" );
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document.write( "Add the 1 and the -56, getting -55 and write that under the -56\r\n" );
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document.write( "-4|1  0  -2   1\r\n" );
document.write( "  |  -4  16 -56\r\n" );
document.write( "   1 -4  14 -55\r\n" );
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document.write( "Now we must interpret the numbers at the bottom.  The last number\r\n" );
document.write( "-55 is the remainder, and the numbers to the left of it are the\r\n" );
document.write( "coefficients of the quotient polynomial which has degree which is\r\n" );
document.write( "one less than the original polynomial:\r\n" );
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document.write( "So the answer is\r\n" );
document.write( "                   -55\r\n" );
document.write( "   x² - 4x + 14 + ------\r\n" );
document.write( "                   x+4\r\n" );
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document.write( "Or if you prefer:\r\n" );
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document.write( "                    55\r\n" );
document.write( "   x² - 4x + 14 - ------\r\n" );
document.write( "                   x+4\r\n" );
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document.write( "The synthetic division is just a shortcut for this long division:\r\n" );
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document.write( "                x² -  4x + 14\r\n" );
document.write( "    x + 4)x³ + 0x² -  2x +  1\r\n" );
document.write( "          x³ + 4x²\r\n" );
document.write( "              -4x² -  2x\r\n" );
document.write( "              -4x² - 16x\r\n" );
document.write( "                     14x +  1\r\n" );
document.write( "                     14x + 56\r\n" );
document.write( "                          -55\r\n" );
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document.write( " which yields the same answer.\r\n" );
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document.write( "Edwin
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