document.write( "Question 695861: The cubic polynomial f(x) is such that the coefficient of x^3 is -1 and the roots of the equation f(x) = 0 are 1, 2 and k. Given that f(x) has a remainder of 8 when divided by x – 3, find
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Algebra.Com's Answer #428656 by KMST(5328) $\"\"$ $\"About$

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The factoring of such a cubic polynomial would be
\n" ); document.write( " $\"f%28x%29=%28-1%29%28x-1%29%28x-2%29%28x-k%29\"$
\n" ); document.write( "so that each factor would be zero for each of the roots of $\"f%28x%29=0\"$ .
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\n" ); document.write( "The remainder of $\"f%28x%29\"$ when divided by $\"%28x-3%29\"$ is
\n" ); document.write( " $\"f%283%29=%28-1%29%283-1%29%283-2%29%283-k%29=8\"$ --> $\"%28-1%29%282%29%281%29%283-k%29=8\"$ --> $\"2k-6=8\"$ --> $\"2k=8%2B6\"$ --> $\"2k=14\"$ --> $\"highlight%28k=7%29\"$
\n" ); document.write( "and $\"f%28x%29=%28-1%29%28x-1%29%28x-2%29%28x-7%29\"$
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\n" ); document.write( "The remainder of $\"f%28x%29\"$ when divided by $\"%28x%2B3%29\"$ is
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