document.write( "Question 1138587: for each polynomial function:
\n" ); document.write( "a)find the rational zeros and all the other zeros; that is solve f(x)=0.
\n" ); document.write( "b)express f(x) as a product of linear factors.\r
\n" ); document.write( "\n" ); document.write( "f(x)=x^4-2x^3-5x^2+4x+6
\n" ); document.write( "(0=x^4-2x^3-5x^2+4x+6) \n" ); document.write( "

Algebra.Com's Answer #756394 by josgarithmetic(39617) $\"\"$ $\"About$

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The possible roots to check for would be -6, -3, -2, -1, 1, 2, 3, 6.
\n" ); document.write( "Using synthetic division to test should indicate 3 and -1 to be the rational roots.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Two more roots to find for the quadratic part left over from the two synthetic divisions (could be two irrational zeros).\r
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "3  |  1   -2   -5   4   6\r\n" );
document.write( "   |       3    3  -6   -6\r\n" );
document.write( "   |___________________________\r\n" );
document.write( "     1    1    -2  -2   0\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "-1  |   1   1   -2   -2\r\n" );
document.write( "    |\r\n" );
document.write( "    |      -1   0     2\r\n" );
document.write( "    |________________________\r\n" );
document.write( "        1  0    -2    0\r\n" );
document.write( "

\n" ); document.write( " $\"%28x%5E2-2%29%5E2=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x%5E2-2=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x%5E2=2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"system%28x=-sqrt%282%29%2Cx=sqrt%282%29%2Cthe_last_two_roots%29\"$ \n" ); document.write( "

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