document.write( "Question 727283: How do you use synthetic division to find which value of k will guarantee that the given binomial is a factor of the polynomial? Here is a problem
\n" ); document.write( "x^3-kx^2-6x+8;x+2 \n" ); document.write( "

Algebra.Com's Answer #445042 by josgarithmetic(39620) $\"\"$ $\"About$

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You literally perform long division on the polynomials. Divide the $\"x%5E3-kx%5E2-6x%2B8\"$ by $\"x%2B2\"$ . Watch each step extremely carefully. In the last subtraction, if you did you algorithm correctly, you should have something equivalent to $\"8-2%282k-2%29=12-4k\"$ , and THIS MUST EQUAL ZERO, if the divisor, $\"x%2B2\"$ is to be a binomial factor of the dividend cubic polynomial. Set $\"12-4k=0\"$ and find $\"k=3\"$ . \n" ); document.write( "

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