document.write( "Question 1034287: 1. A polynomial function is shown below.
\n" ); document.write( " f(x) = x^6 + 12x^5 + 43x^4 + 22x^3 - 138x^2 - 280x -200\r
\n" ); document.write( "\n" ); document.write( " a. Find the real zeros of f (x).
\n" ); document.write( " b. Express f (x) in terms of linear factors.
\n" ); document.write( " c. Find all of the zeros of f (x).
\n" ); document.write( " (3 points)
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Algebra.Com's Answer #649028 by josgarithmetic(39617)\"\" \"About 
You can put this solution on YOUR website!

\n" ); document.write( "Rational Roots Theorem with synthetic division indicate possible zeros to check are the positive and negative
\n" ); document.write( "of 1,2,4,5,8,10,25,50,100. A graphing tool might help to decide which of the possibilities to try first.\r
\n" ); document.write( "\n" ); document.write( "Here are some of the productive synthetic-division root checkings. The first dividend of coefficients to start is
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 1  12  43  22  -138  -280  -200
; the roots being checked are shown to the left, in the \"divisor\" location.\r
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document.write( " -2 |    1    12    43    22    -138    -280   -200\r\n" );
document.write( "    |\r\n" );
document.write( "    |          -2   -20   -46     48     180    200\r\n" );
document.write( "    |____________________________________________________\r\n" );
document.write( "         1    10    23    -24     -90    -100    0\r\n" );
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document.write( " -5 |    1    10    23    -24    -90    -100\r\n" );
document.write( "    |\r\n" );
document.write( "    |         -5    -25    10    70      100\r\n" );
document.write( "    |____________________________________________________\r\n" );
document.write( "        1     5    -2     -14    -20      0\r\n" );
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document.write( " -5 |     1     5    -2     -14    -20   \r\n" );
document.write( "    |\r\n" );
document.write( "    |          -5    0       10     20\r\n" );
document.write( "    |____________________________________\r\n" );
document.write( "          1    0      -2     -4     0\r\n" );
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document.write( " 2  |     1    0      -2     -4\r\n" );
document.write( "    |\r\n" );
document.write( "    |          2      4       4\r\n" );
document.write( "    |______________________________\r\n" );
document.write( "          1    2      2      0\r\n" );
document.write( "

\n" ); document.write( "This last quotient, having remainder 0, indicates the polynomial factor \"x%5E2%2B2x%2B2\"
\n" ); document.write( "and the zeros are found using general solution formula of a quadratic equation.\r
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\n" ); document.write( "\n" ); document.write( "Zeros are \"%28-2%2B-+sqrt%282%5E2-4%2A2%29%29%2F2\"\r
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\n" ); document.write( "\n" ); document.write( "\"%28-2%2B-+sqrt%284-8%29%29%2F2\"\r
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\n" ); document.write( "\n" ); document.write( "\"%28-2%2B-+sqrt%28-4%29%29%2F2\"\r
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\n" ); document.write( "\n" ); document.write( "\"%28-2%2B-+2%2Asqrt%28-1%29%29%2F2\"\r
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\n" ); document.write( "\n" ); document.write( "\"highlight%28-1%2B-+i%29\"\r
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\n" ); document.write( "To summarize all of these zeros-finding results,
\n" ); document.write( "REAL RATIONAL ZEROS:
\n" ); document.write( "-5 of multiplicity two;
\n" ); document.write( "-2
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\n" ); document.write( "COMPLEX ZEROS:
\n" ); document.write( "-1-i and -1+i
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\n" ); document.write( "\n" ); document.write( "To begin in forming the factorized form of your function, start with this, and then simplify the complex part if you want.
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