document.write( "Question 820446: Using synthetic division can someone help me determine the quotient to these problems?\r
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Algebra.Com's Answer #493583 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
1. F(x)=2x³+8x²-5x+5; G(x)=x-2
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document.write( "Synthetic division gives you an easier way to do two \r\n" );
document.write( "different things:\r\n" );
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document.write( "A. An easier way to divide a polynomial by a binomial of\r\n" );
document.write( "the form x±↏, where there is a number in the box. The \r\n" );
document.write( "sign can either be + or -.\r\n" );
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document.write( "B. An easier way to substitute a number in a polynomial.\r\n" );
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document.write( "1. F(x)=2x³+8x²-5x+5; G(x)=x-2\r\n" );
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document.write( "Change the sign of the -2 to +2\r\n" );
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document.write( "2|2  8 -5  5\r\n" );
document.write( " |   4 24 38 \r\n" );
document.write( "  2 12 19 43\r\n" );
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document.write( "The numbers across the bottom all except the last one\r\n" );
document.write( "tells you the coefficients of the quotient.  The last\r\n" );
document.write( "number is the remainder.  \r\n" );
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document.write( "The quotient is always one degree less than the original\r\n" );
document.write( "polynomial.  The original polynomial is degree 3 so\r\n" );
document.write( "the quotient polynomial will be degree 2\r\n" );
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document.write( "2x²+12x+19 with remainder 43\r\n" );
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document.write( "or you can write it  2x²+12x+19+\"43%2F%28x-2%29\" \r\n" );
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document.write( "It is a shortcut for this long division:\r\n" );
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document.write( "         2x²+12x+19      \r\n" );
document.write( "x-2)2x³+ 8x²- 5x+ 5\r\n" );
document.write( "    2x³- 4x²\r\n" );
document.write( "        12x²- 5x\r\n" );
document.write( "        12x²-24x\r\n" );
document.write( "             19x+ 5\r\n" );
document.write( "             19x-38\r\n" );
document.write( "                 43\r\n" );
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document.write( "f(x)=x4-x²+3x; g(x)=x+1\r\n" );
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document.write( "This one is like the first one except that you must put in\r\n" );
document.write( "two zero placeholders\r\n" );
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document.write( "You must consider f(x) as this:\r\n" );
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document.write( "f(x) = x4-0x3-x2+3x+0\r\n" );
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document.write( "and start with this:\r\n" );
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document.write( "-1| 1  0 -1  3  0\r\n" );
document.write( "  |______________\r\n" );
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document.write( "You finish it.\r\n" );
document.write( "       \r\n" );
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document.write( "f(x)= -15x³+18x²-x+2 at x=-2\r\n" );
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document.write( "This is the other use for synthetic division. A shortcut\r\n" );
document.write( "for substituting into a polynomial:\r\n" );
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document.write( "Uss the same value -2 (do not change the sign)\r\n" );
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document.write( "-2|-15  18  -1    2\r\n" );
document.write( "  |     30 -96  194\r\n" );
document.write( "   -15  48 -97  196\r\n" );
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document.write( "The answer is the remainder 196. (Ignore the other numbers)\r\n" );
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document.write( "That's a shortcut for this substitution for x and simplifying: \r\n" );
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document.write( "f(x)= -15x³+18x²-x+2 at x=-2\r\n" );
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document.write( "f(-2) = -15(-2)³+18(-2)²-(-2)+2\r\n" );
document.write( "f(-2) = -15(-8)+36(4)+2+2\r\n" );
document.write( "f(-2) = 120+72+2+2\r\n" );
document.write( "f(-2) = 196\r\n" );
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document.write( "Edwin
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