document.write( "Question 695485: Given that x – p is a factor of the expression x^2-(p+2)x-p^2+4p+8 , calculate the possible values of p. \n" ); document.write( "

Algebra.Com's Answer #428513 by mouk(232) $\"\"$ $\"About$

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Let $\"+f%28x%29=x%5E2-%28p%2B2%29x-p%5E2%2B4p%2B8+\"$
\n" ); document.write( "By the remainder theorem $\"+x-p+\"$ is a factor of $\"+f%28x%29+\"$ if and only if $\"+f%28p%29=0+\"$ \r
\n" ); document.write( "\n" ); document.write( "So $\"+f%28p%29=0+\"$ implies:
\n" ); document.write( " $\"+p%5E2-%28p%2B2%29p-p%5E2%2B4p%2B8++=+0+\"$
\n" ); document.write( " $\"+p%5E2+-+p%5E2+-+2p+-p%5E2+%2B+4p+%2B+8++=+0+\"$
\n" ); document.write( " $\"+2p+-p%5E2+%2B+8++=+0+\"$
\n" ); document.write( " $\"+p%5E2+-2p+-8+=+0+\"$
\n" ); document.write( " $\"+%28p-4%29%28p%2B2%29+=+0+\"$
\n" ); document.write( "Giving $\"+p=4+\"$ or $\"+p=-2+\"$ \r
\n" ); document.write( "\n" ); document.write( "Check:
\n" ); document.write( "======
\n" ); document.write( "When p=4 we expect $\"+x-4+\"$ to be a factor:
\n" ); document.write( "

\n" ); document.write( "so $\"+x-4+\"$ is a factor\r
\n" ); document.write( "\n" ); document.write( "When p=-2 we expect $\"+x-%28-2%29+=+x%2B2+\"$ to be a factor:
\n" ); document.write( "

\n" ); document.write( "so $\"+x%2B2+\"$ is a factor \n" ); document.write( "

\n" );