document.write( "Question 1183612: Find the values of k if 3(x+3)^4 - (k+x)^2 has a factor x+1 \n" ); document.write( "

Algebra.Com's Answer #814019 by KMST(5328) $\"\"$ $\"About$

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If a polynomial in $\"x\"$ has $\"x%2B1\"$ as a factor, it can be written as $\"%28x%2B1%29Q%28x%29\"$ where $\"Q%28x%29\"$ is another polynomial,
\n" ); document.write( "and the value of the original polynomial is
\n" ); document.write( " $\"%28-1%2B1%29Q%28-1%29=0%2AQ%28-1%29=0\"$ for $\"x=-1\"$
\n" ); document.write( "Then, for $\"x=-1\"$ we have
\n" ); document.write( " $\"3%28-1%2B3%29%5E4-%28k%2B%28-1%29%29%5E2=0\"$
\n" ); document.write( " $\"3%282%29%5E4-%28k-1%29%5E2=0\"$
\n" ); document.write( " $\"3%2A16-%28k-1%29%5E2=0\"$
\n" ); document.write( " $\"%28k-1%29%5E2=3%2A16\"$
\n" ); document.write( " $\"k-1=%22+%22+%2B-+sqrt%283%2A16%29\"$
\n" ); document.write( " $\"k=1+%2B-+sqrt%283%2A16%29\"$
\n" ); document.write( " $\"highlight%28k=1+%2B-+4sqrt%283%29%29\"$
\n" ); document.write( "
\n" ); document.write( "You can also solve the problem the long, cumbersome, treacherous way, but that increases the risk of errors. \n" ); document.write( "

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