document.write( "Question 1077689: Find an ordered pair of constants (a,b) such that the polynomial f(x)=x^3+ax^2+(b+2)x+1 is divisible by x^2-1.\r
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Algebra.Com's Answer #692202 by KMST(5328) $\"\"$ $\"About$

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To be divisible by $\"x%5E2-1=%28x%2B1%29%28x-1%29\"$ ,
\n" ); document.write( " $\"f%28x%29\"$ must be divisible by $\"%28x%2B1%29\"$ , and by $\"%28x-1%29\"$ .
\n" ); document.write( "That means that it must be true that $\"f%28-1%29=0\"$ and that $\"f%281%29=0\"$ .
\n" ); document.write( " $\"f%28-1%29=%28-1%29%5E3%2Ba%28-1%29%5E2%2B%28b%2B2%29%28-1%29%2B1=-1%2Ba-b-2%2B1=a-b-2\"$
\n" ); document.write( " $\"f%281%29=1%2Ba%2Bb%2B2%2B1=a%2Bb%2B4\"$ .
\n" ); document.write( " $\"system%28a-b-2=0%2Ca%2Bb%2B4=0%29\"$ --> $\"system%28a-b-2=0%2Ca-b-2%2Ba%2Bb%2B4=0%29\"$ --> $\"system%28b=a-2%2C2a%2B2=0%29\"$ --> $\"system%28b=a-2%2C2a=-2%29\"$ --> $\"system%28b=a-2%2Ca=-1%29\"$ --> $\"system%28b=-1-2%2Ca=-3%29\"$ --> $\"highlight%28system%28b=-3%2Ca=-1%29%29\"$ \n" ); document.write( "

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