.
The solution by the tutor @MathLover1 not only is INCORRECT - it is IRRELEVANT, because it operates
with WRONG CONCEPTIONS. Unfortunately. Below find the correct solution.
From the condition, it should be clear to you that the quotient of division the 3-rd degree polynomial x^3 + ax + b
by the quadratic polynomial (x^2-1) is a linear polynomial of the form (x+c) with the leading coefficient 1
and the constant term c, now unknown to us. So
x^3 + ax + b = (x^2-1)*(x+c) + (x+2).
Now make FOIL, combine like terms and then compare coefficients:
x^3 + ax + b = x^3 -x + cx^2 - c + x + 2 = x^3 + cx^2 + 2-c.
Comparing coefficients, you see that c= 0 (look in x^2 !); a= 0 and b= 2.
Answer. a= 0 and b= 2.
Solved.
---------------
I estime the tutor @MathLover1 very high - she rarely makes mistakes.
But even first class tutor is not guaranteed of making mistakes - sometimes :)