document.write( "Question 148851: Use the rational roots theorem to solve:
\n" ); document.write( "p(x)=x^4-5x^3+5x^2+5x-6 \n" ); document.write( "
Algebra.Com's Answer #110220 by Edwin McCravy(20056) $\"\"$ $\"About$
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document.write( "Use the rational roots theorem to solve:\r\n" );
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document.write( "The last term is -6, which in absolute value is 6, and which\r\n" );
document.write( "has these factors 1,2,3,6\r\n" );
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document.write( "The leading term (the term with largest exponent) is , has\r\n" );
document.write( "coefficient 1, which in absolute value is 1, and which\r\n" );
document.write( "has only the one factor 1.\r\n" );
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document.write( "Now we form all the fractions with numerator 1,2,3,or 6 and\r\n" );
document.write( "denominator 1\r\n" );
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document.write( "These are , , ,  or\r\n" );
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document.write( "          , , , .\r\n" );
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document.write( "Their negatives are also possible rational roots, so all the\r\n" );
document.write( "possible rational roots are:\r\n" );
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document.write( "          ą, ą, ą, ą \r\n" );
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document.write( "We start out by trying  using synthetic division to\r\n" );
document.write( "see if we get a 0 remainder:\r\n" );
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document.write( "      1| 1 -5  5  5 -6\r\n" );
document.write( "       |    1 -4  1  6\r\n" );
document.write( "         1 -4  1  6  0\r\n" );
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document.write( "Yes we do get 0 remainder, so we know that we have factored\r\n" );
document.write( "the polynomial\r\n" );
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document.write( "   as\r\n" );
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document.write( "So now we can just find the roots of the simpler polynomial:\r\n" );
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document.write( "The first and last numbers happen to be the same as they were\r\n" );
document.write( "in the original, so we can try the same ones again.  We try 1\r\n" );
document.write( "again:\r\n" );
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document.write( "      1| 1 -4  1  6\r\n" );
document.write( "       |    1 -3 -2\r\n" );
document.write( "         1 -3 -2  4  \r\n" );
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document.write( "No that leaves a remainder of 4, not 0.\r\n" );
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document.write( "So we try -1\r\n" );
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document.write( "     -1| 1 -4  1  6\r\n" );
document.write( "       |   -1  6 -6\r\n" );
document.write( "         1 -5  6  0\r\n" );
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document.write( "Yes we do get 0 remainder, so we know that we have factored\r\n" );
document.write( "the polynomial again.\r\n" );
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document.write( "First we factored\r\n" );
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document.write( "  \r\n" );
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document.write( "   as\r\n" );
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document.write( "  \r\n" );
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document.write( "Now we have factored the polynomial in the \r\n" );
document.write( "second parentheses, and we have:\r\n" );
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document.write( "So now we can just find the roots of the simpler polynomial:\r\n" );
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document.write( "     \r\n" );
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document.write( "But we don't need to do synthetic division again, for\r\n" );
document.write( " factors as \r\n" );
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document.write( "So now we have factored  completely:\r\n" );
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document.write( "Set each factor equal to 0 and so the roots are \r\n" );
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document.write( ", , , \r\n" );
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document.write( "Edwin
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