document.write( "Question 1058801: Use the factor theorem to prove that x^2 - x - 2 is a factor of x^3 - 6x^2 +3x + 10 \n" ); document.write( "

Algebra.Com's Answer #673910 by josgarithmetic(39617) $\"\"$ $\"About$

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What happens if you divide $\"x%5E3-6x%5E2%2B3x%2B10\"$ by $\"x%5E2-x-2\"$ ?\r
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document.write( "x^2-x-2    |     x      -5\r\n" );
document.write( "           -------------------------------------------\r\n" );
document.write( "                x^3    -6x^2    +3x    +10\r\n" );
document.write( "                x^3    -x^2     -2x\r\n" );
document.write( "                ____________________\r\n" );
document.write( "                0      -5x^2    5x     10\r\n" );
document.write( "                       -5x^2   5x      10\r\n" );
document.write( "                       -------------------\r\n" );
document.write( "                       0         0     0

Remainder is 0. The divisor IS a factor of the dividend.\r
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\n" ); document.write( "\n" ); document.write( "As an alternative, what happens if you substitute the given divisor INTO the cubic polynomial dividend and simplify? That work will be much longer; the division shown above is easier. \n" ); document.write( "

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