SOLUTION: 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. Enter your answer as an ordered pair in the format (a,b)

Algebra ->  Exponents -> SOLUTION: 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. Enter your answer as an ordered pair in the format (a,b)      Log On


   

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.
Enter your answer as an ordered pair in the format (a,b)
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
To be divisible by x%5E2-1=%28x%2B1%29%28x-1%29 ,
f%28x%29 must be divisible by %28x%2B1%29 , and by %28x-1%29 .
That means that it must be true that f%28-1%29=0 and that f%281%29=0 .
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
f%281%29=1%2Ba%2Bb%2B2%2B1=a%2Bb%2B4 .
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