document.write( "Question 820318: Find k such that f(x)=x^3-kx^2+kx+2 has the factor x-2.
\n" ); document.write( "I have no idea what this is and my final is due in a few hours! help me please!
\n" ); document.write( "I know I have to divide by x-2 but I don't know how to do so or what to do after that. \n" ); document.write( "

Algebra.Com's Answer #493457 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"f%28x%29=x%5E3-kx%5E2%2Bkx%2B2\"$
\n" ); document.write( "First of all, this is a polynomial, not a rational function (which has x in denominator(s)). Please post your problems in a relevant category.

\n" ); document.write( "And yes, you will divide. Synthetic division is easiest:
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document.write( "2 |   1   -k     k  2\r\n" );
document.write( "---        2  4-2k  8-2k\r\n" );
document.write( "     --------------------\r\n" );
document.write( "      1  2-k  4-k   10-2k\r\n" );
document.write( "

Since x-2 is supposed to be a factor, then we should get a remainder of zero when we divide. The remainder we got, 10-2k, must then be zero:
\n" ); document.write( "10-2k = 0
\n" ); document.write( "Adding 2k:
\n" ); document.write( "10 = 2k
\n" ); document.write( "Dividing by 2:
\n" ); document.write( "5 = k
\n" ); document.write( "This is the value for k that makes x-2 a factor of f(x). \n" ); document.write( "

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