document.write( "Question 1183611: For what value of k is x^3 - 2kx^2 + 3x + k exactly divisible by x-2 \n" ); document.write( "

Algebra.Com's Answer #814020 by KMST(5328) $\"\"$ $\"About$

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When you divide that polynomial $\"P%28x%29=x%5E3+-+2kx%5E2+%2B+3x+%2B+k\"$ by $\"x-2\"$ the quotient is $\"Q%28x%29\"$ , another polynomial of degree 2.
\n" ); document.write( "In other words $\"P%28x%29=%28x-2%29%2AQ%28x%29\"$ for every value of $\"x\"$
\n" ); document.write( "and so for $\"x=2\"$ we have $\"P%282%29=%282-2%29%2AQ%28x%29=0%2AQ%28x%29=0\"$ .
\n" ); document.write( "So,
\n" ); document.write( " $\"2%5E3+-+2k2%5E2+%2B+3%2A2+%2B+k=0\"$
\n" ); document.write( " $\"8+-+2k%2A4+%2B+6+%2B+k=0\"$
\n" ); document.write( " $\"14+-+8k+%2B+k=0\"$
\n" ); document.write( " $\"14+-+7k=0\"$ --> $\"highlight%28k=14%2F7%29\"$ \n" ); document.write( "

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