document.write( "Question 1131131: What are the steps to solving a problem that’s states :
\n" ); document.write( "X^4 - 4x^3 - 6x^2 + 36x - 27 has a factor of (x-3) with a multiplicity of two ? \n" ); document.write( "

Algebra.Com's Answer #747750 by josgarithmetic(39800) $\"\"$ $\"About$

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Rational Roots Theorem indicates possible roots to check are -27, -9, -3, -1, 1, 3, 9, 27.\r
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\n" ); document.write( "\n" ); document.write( "Try using synthetic division to check for any or all of them. Remainder 0 means, the checked value is a root of the given polynomial.\r
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\n" ); document.write( "\n" ); document.write( "x-3 factor is the root or zero, 3.\r
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document.write( "3   |   1   -4   -6   36   -27\r\n" );
document.write( "    |       3    -3  -27    27\r\n" );
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document.write( "        1   -1   -9   9      0\r\n" );
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document.write( "Test again using the resulting coefficients from that result.\r\n" );
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document.write( "3    |    1   -1   -9   9\r\n" );
document.write( "     |   \r\n" );
document.write( "     |         3    6  -9\r\n" );
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document.write( "         1    2    -3   0\r\n" );
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document.write( "Resulting coefficients now mean  \r\n" );
document.write( "which factorizes as  \r\n" );
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\n" ); document.write( "The full factorization of the given polynomial is $\"highlight%28%28x-3%29%5E2%28x%2B3%29%28x-1%29%29\"$ . \n" ); document.write( "

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