document.write( "Question 89434: Divide by using synthetic division \"Divide+by+using+synthetic+division+\" (x^3 + 3x^2 -34x + 48) divided by (x - 3) \n" ); document.write( "
Algebra.Com's Answer #65020 by Edwin McCravy(20056)\"\" \"About 
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document.write( "Divide by using synthetic division\r\n" );
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document.write( "(x³ + 3x² - 34x + 48) divided by (x - 3)\r\n" );
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document.write( "Put a 1 before the first term.  It is already\r\n" );
document.write( "in descending order.\r\n" );
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document.write( "1x³ + 3x² - 34x + 48\r\n" );
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document.write( "Erase the variables:\r\n" );
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document.write( "From (x - 3), change the sign of -3 to +3, or 3, and write this:\r\n" );
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document.write( " 3|1   3 -34  48\r\n" );
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document.write( "Bring down the 1\r\n" );
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document.write( " 3|1   3 -34  48\r\n" );
document.write( "  |             \r\n" );
document.write( "   1\r\n" );
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document.write( "Multiply the 1 at the bottom by the 3 on the far left, getting\r\n" );
document.write( "3, and so  we put the 3 ABOVE AND TO THE RIGHT OF the 1 we just\r\n" );
document.write( "brought down.  So we have this:\r\n" );
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document.write( " 3|1   3 -34  48\r\n" );
document.write( "  |    3        \r\n" );
document.write( "   1\r\n" );
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document.write( "Now we add the column with the 3 and the 3 and get 6. So we write\r\n" );
document.write( "that 6 under the two 3's we just added,\r\n" );
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document.write( " 3|1   3 -34  48\r\n" );
document.write( "  |    3              \r\n" );
document.write( "   1   6 \r\n" );
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document.write( "Now we add the column with the 3 and the 3 and get 6. So we write\r\n" );
document.write( "that 6 under the two 3's we just added,\r\n" );
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document.write( "Now we multiply the 6 by the 3 at the far left, getting 18, and write\r\n" );
document.write( "that ABOVE AND TO THE RIGHT of the 6\r\n" );
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document.write( " 3|1   3 -34  48\r\n" );
document.write( "  |    3  18          \r\n" );
document.write( "   1   6 \r\n" );
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document.write( "Now we add the -34 and the 18 and get -16, so we write that under\r\n" );
document.write( "their column:\r\n" );
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document.write( " 3|1   3 -34  48\r\n" );
document.write( "  |    3  18          \r\n" );
document.write( "   1   6 -16 \r\n" );
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document.write( "Then we multiply the -16 by the 3 at the far left, getting -48.\r\n" );
document.write( "Then we write that ABOVE AND TO THE RIGHT of -16:\r\n" );
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document.write( " 3|1   3 -34  48\r\n" );
document.write( "  |    3  18 -48      \r\n" );
document.write( "   1   6 -16    \r\n" );
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document.write( "Only one more thing to do.  Combine the 48 and the -48 and get 0.\r\n" );
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document.write( " 3|1   3 -34  48\r\n" );
document.write( "  |    3  18 -48      \r\n" );
document.write( "   1   6 -16   0\r\n" );
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document.write( "Now we have to interpret the synthetic answer:\r\n" );
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document.write( "The last number, 0 is the remainder.\r\n" );
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document.write( "The other three numbers \r\n" );
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document.write( "   1   6 -16\r\n" );
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document.write( "are a synthetic form of the quotient, remembering \r\n" );
document.write( "it will be a polynomial of one less degree than \r\n" );
document.write( "the original polynomial. So since the original \r\n" );
document.write( "polynomial has degree 3, it will have degree 2 \r\n" );
document.write( "and so will begin with an x² term. So the\r\n" );
document.write( "quotient i\r\n" );
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document.write( "   1   6 -16\r\n" );
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document.write( "   |   |  |\r\n" );
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document.write( "   1x²+6x-16\r\n" );
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document.write( "Then we write the answer and we would put the remainder\r\n" );
document.write( "over the divisor:\r\n" );
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document.write( " x² + 6x - 16 \r\n" );
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document.write( "Edwin
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