document.write( "Question 988995: 1.)When the expression x^3+mx^2+nx-5 is divided by x+2 and x+3, the remainders are 2 and 13 respectively. Find the values of m and n.\r
\n" ); document.write( "\n" ); document.write( "2)When P(x)=x^2+ax-b is divided by x-1, the remainder is 6. When P(x) is divided by x+2, the remainder is 3. Find the values of a and b.\r
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Algebra.Com's Answer #609445 by KMST(5328) $\"\"$ $\"About$

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When a polynomial $\"P%28x%29\"$ is divided by $\"x-k\"$ (where $\"k\"$ is any real number) is $\"P%28k%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "1) $\"P%28-2%29=%28-2%29%5E3%2Bm%28-2%29%5E2%2Bn%28-2%29-5=-8%2B4m-2n-5=4m-2n-13\"$
\n" ); document.write( "If the remainder is $\"2\"$ when $\"P%28x%29=x%5E3%2Bmx%5E2%2Bnx-5\"$ is divided by $\"x%2B2=x-%28-2%29%29\"$ ,
\n" ); document.write( "then $\"4m-2n-13=2\"$ ---> $\"4m-2n=15\"$ .
\n" ); document.write( " $\"P%28-3%29=%28-3%29%5E3%2Bm%28-3%29%5E2%2Bn%28-3%29-5=-27%2B9m-3n-5=9m-3n-32\"$
\n" ); document.write( "If the remainder is $\"13\"$ when $\"P%28x%29=x%5E3%2Bmx%5E2%2Bnx-5\"$ is divided by $\"x%2B3=x-%28-3%29%29\"$ ,
\n" ); document.write( "then $\"9m-3n-32=13\"$ ---> $\"9m-3n=45\"$ ---> $\"3m-n=15\"$ ---> $\"n=3m-15\"$ .
\n" ); document.write( " $\"system%28n=3m-15=45%2C4m-2n=15%29\"$ ---> $\"system%28n=3m-15=45%2C4m-2%283m-15%29=15%29\"$ ---> $\"system%28n=3m-15=45%2C4m-6m%2B30=15%29\"$
\n" ); document.write( "---> $\"system%28n=3m-15=45%2C-2m%2B30=15%29\"$ ---> $\"system%28n=3m-15=45%2C-2m-30=15%29\"$ ---> $\"system%28n=3m-15=45%2Cm=15%2F2%29\"$
\n" ); document.write( "---> $\"system%28n=3%2815%2F2%29-15=45%2Cm=15%2F2%29\"$ ---> $\"system%28n=45%2F2-30%2F2=45%2Cm=15%2F2%29\"$ ---> $\"highlight%28system%28n=15%2F2%2Cm=15%2F2%29%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "2) Similarly,
\n" ); document.write( " $\"P%281%29=1%5E2%2Ba%2A1-b=1%2Ba-b=6\"$ ---> $\"a-b=6-1\"$ ---> $\"a-b=5\"$
\n" ); document.write( "and $\"P%28-2%29=%28-2%29%5E2%2Ba%2A%28-2%29-b=4-2a-b=3\"$ ---> $\"-2a-b=3-4\"$ ---> $\"-2a-b=-1\"$ ---> $\"2a%2Bb=1\"$
\n" ); document.write( " $\"system%28a-b=5%2C2a%2Bb=1%29\"$ ---> $\"system%28a-b=5%2Ca-b%2B2a%2Bb=5%2B1%29\"$ ---> $\"system%28a-b=5%2C3a=6%29\"$ ---> $\"system%28a-b=5%2Ca=2%29\"$ ---> $\"system%282-b=5%2Ca=2%29\"$ ---> $\"system%28-b=3%2Ca=2%29\"$ ---> $\"highlight%28system%28b=-3%2Ca=2%29%29\"$ \n" ); document.write( "

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