9514 1404 393
Answer:
Step-by-step explanation:
Subtracting the remainder from the original polynomial gives a polynomial that has (x^2 -1) as a factor. Dividing, we find the quotient and remainder to be ...
(x^5 +ax^3 +bx^2 +x -1)/(x^2 -1) = (x^3 +(1+a)x +b) remainder (2+a)x +(b -1)
Since we want the remainder to be zero, we require ...
2+a = 0 ⇒ a = -2
b -1 = 0 ⇒ b = 1
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The attachment shows the division as given in the problem statement (with the given remainder expression).
