document.write( "Question 920397: Use the factor theorem and synthetic division to determine whether or not the first polynomial is a factor of the second. \r
\n" ); document.write( "\n" ); document.write( "(x+1); x^4 - x^3 - 2x^2 + 7x + 7\r
\n" ); document.write( "\n" ); document.write( "I also worked on this myself and got this:\r
\n" ); document.write( "\n" ); document.write( "(-1)^4 - (-1)^3 - 2(-1)^2 + 7(-1) + 7, which turns into...
\n" ); document.write( "... 1 + 1 - 2 - 7 + 7 = 0, meaning (x + 1) IS a factor, I think? But I haven't gone into synthetic division, and I could be wrong. Please correct me if I am, thank you! \n" ); document.write( "
Algebra.Com's Answer #558342 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Here's what you are supposed to do:\r\n" );
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document.write( "Start with the coefficients of the terms\r\n" );
document.write( "and this array:\r\n" );
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document.write( "-1| 1 -1 -2  7  7\r\n" );
document.write( "  |______________\r\n" );
document.write( "    \r\n" );
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document.write( "Bring down the 1 down below the line\r\n" );
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document.write( "-1| 1 -1 -2  7  7\r\n" );
document.write( "  |                 \r\n" );
document.write( "    1 \r\n" );
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document.write( "Multiply that 1 by the -1 at the far left, getting -1\r\n" );
document.write( "Place it above and to the right of that 1:\r\n" );
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document.write( "-1| 1 -1 -2  7  7\r\n" );
document.write( "  |   -1          \r\n" );
document.write( "    1  \r\n" );
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document.write( "Add the -1 and the -1 getting -2 and write it below the line.\r\n" );
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document.write( "-1| 1 -1 -2  7  7\r\n" );
document.write( "  |   -1         \r\n" );
document.write( "    1 -2  \r\n" );
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document.write( "Multiply that -2 by the -1 at the far left, getting 2\r\n" );
document.write( "Place it above and to the right of that -2:\r\n" );
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document.write( "-1| 1 -1 -2  7  7\r\n" );
document.write( "  |   -1  2        \r\n" );
document.write( "    1 -2  \r\n" );
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document.write( "Add the -2 and the 2 getting 0 and write it below the line.\r\n" );
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document.write( "-1| 1 -1 -2  7  7\r\n" );
document.write( "  |   -1  2        \r\n" );
document.write( "    1 -2  0  \r\n" );
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document.write( "Multiply that 0 by the -1 at the far left, getting 0\r\n" );
document.write( "Place it above and to the right of that 0:\r\n" );
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document.write( "-1| 1 -1 -2  7  7\r\n" );
document.write( "  |   -1  2  0    \r\n" );
document.write( "    1 -2  0  \r\n" );
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document.write( "Add the 7 and the 0 getting 7 and write it below the line.\r\n" );
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document.write( "-1| 1 -1 -2  7  7\r\n" );
document.write( "  |   -1  2  0    \r\n" );
document.write( "    1 -2  0  7  \r\n" );
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document.write( "Multiply that 7 by the -1 at the far left, getting -7\r\n" );
document.write( "Place it above and to the right of that 7:\r\n" );
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document.write( "-1| 1 -1 -2  7  7\r\n" );
document.write( "  |   -1  2  0 -7\r\n" );
document.write( "    1 -2  0  7  \r\n" );
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document.write( "Add the 7 and the -7 getting 0 and write it below the line.\r\n" );
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document.write( "-1| 1 -1 -2  7  7\r\n" );
document.write( "  |   -1  2  0 -7\r\n" );
document.write( "    1 -2  0  7  0\r\n" );
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document.write( "Now you've finished the synthetic division.  The 0 on the bottom\r\n" );
document.write( "right tells you that the remainder is 0, and that x+1 is indeed a\r\n" );
document.write( "factor.  The other numbers before that 0 on the far right,\r\n" );
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document.write( "    1 -2  0  7  \r\n" );
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document.write( "tell you the coefficients of the quotient you would get if you did \r\n" );
document.write( "the problem by long division instead of synthetic division.\r\n" );
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document.write( "The quotient is a polynomial of 1 degree less than the degree of\r\n" );
document.write( "the original polynomial with those coefficients. The original\r\n" );
document.write( "polynomial was of degree 4, so the quotient is of degree 3, so\r\n" );
document.write( "using those numbers as coefficients, you have the quotient as:\r\n" );
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document.write( "    1x3-2x2+0x+7\r\n" );
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document.write( "or just\r\n" );
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document.write( "    x3-2x2+7\r\n" );
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document.write( "Which means you have now factored the polynomial as\r\n" );
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document.write( "(x+1)(x3-2x2+7)\r\n" );
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document.write( "Edwin
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