document.write( "Question 232400: If ( x + 3) is a factor of x^3 - 2kx + k^2 , then k is: \n" ); document.write( "

Algebra.Com's Answer #171880 by jsmallt9(3758) $\"\"$ $\"About$

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If ( x + 3) is a factor of $\"x%5E3+-+2kx+%2B+k%5E2\"$ , then (x+3) will divide into $\"x%5E3+-+2kx+%2B+k%5E2\"$ evenly. And synthetic division is probably the easiest way to find out if (x+3) divides evenly:
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document.write( "-3 |  1   0   -2k   k^2\r\n" );
document.write( "----     -3    9  -27+6k               \r\n" );
document.write( "     -----------------------\r\n" );
document.write( "      1  -3  9-2k   k^2+6k-27\r\n" );
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\n" ); document.write( "When a division works out evenly, the remainder is zero. So the value(s) of k that makes $\"k%5E2%2B6k-27\"$ zero will be our answer(s):
\n" ); document.write( " $\"k%5E2%2B6k-27+=+0\"$
\n" ); document.write( "This is a quadratic equation which we can solve by factoring or with the quadratic formula. It factors pretty easily:
\n" ); document.write( " $\"%28k%2B9%29%28k-3%29+=+0\"$
\n" ); document.write( "By the Zero Product Property one of these factor must be zero:
\n" ); document.write( " $\"k%2B9+=+0\"$ or $\"k-3+=+0\"$
\n" ); document.write( "Solving these we get:
\n" ); document.write( " $\"k+=+-9\"$ or $\"k+=+3\"$
\n" ); document.write( "So we have two possible values for k. \n" ); document.write( "

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