document.write( "Question 260983: Use synthetic division and the Factor Theorem to determine whether (x + 1/2) is a factor of P(x) = 10x^4 + 9x^3 – 4x^2 + 9x +6. \n" ); document.write( "

Algebra.Com's Answer #192294 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
(I'm going to use 0.5 instead of 1/2 to make things easier for me.)
\n" ); document.write( "(x+0.5) is a factor of a polynomial if it divides evenly (IOW the remainder is zero) into the polynomial. So all we have to do is divide the polynomial by (x+0.5) and see if the remainder is zero:
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document.write( "-0.5 |   10    9   -4   9   6\r\n" );
document.write( "------        -5   -2   3  -6\r\n" );
document.write( "         ---------------------\r\n" );
document.write( "         10    4   -6  12   0\r\n" );
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\n" ); document.write( "The remainder is 0. So (x + 0.5) is a factor of P(x). (The other factor, taken from the numbers in front of the remainder, is $\"10x%5E3+%2B4x%5E2+-6x+%2B12\"$ \n" ); document.write( "

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