document.write( "Question 756502: If x+a is a factor of the polynomial x^2 + px + q and x^2 + mx + n, then prove that a = (n-q) / (m-p). \n" ); document.write( "

Algebra.Com's Answer #460258 by KMST(5328) $\"\"$ $\"About$

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If $\"x%2Ba\"$ is a factor in
\n" ); document.write( " $\"f%28x%29=x%5E2+%2B+px+%2B+q\"$ and in
\n" ); document.write( " $\"g%28x%29=x%5E2+%2B+mx+%2B+n\"$ , then
\n" ); document.write( " $\"f%28-a%29=a%5E2+-pa%2B+q=0\"$ and
\n" ); document.write( " $\"g%28-a%29=a%5E2+-+ma+%2B+n=0\"$ .
\n" ); document.write( "That would give as a system of equations that looks confusing, but we only need to solve it partially.
\n" ); document.write( " $\"system%28a%5E2+-pa%2B+q=0%2Ca%5E2+-+ma+%2B+n=0%29\"$ --> $\"a%5E2+-pa%2B+q=a%5E2+-+ma+%2B+n\"$ --> $\"-pa%2B+q=-+ma+%2B+n\"$ --> $\"-pa%2B+q%2Bma=n\"$ --> $\"-pa%2Bma=n-q\"$ --> $\"ma-pa=n-q\"$ --> $\"+%28m-p%29a=n-q\"$ --> $\"highlight%28a=%28n-q%29%2F%28m-p%29%29\"$ \n" ); document.write( "

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