Question 1127209
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            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.



<pre>
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.


<U>Answer</U>.  a= 0  and b= 2.
</pre>

Solved.


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I estime the tutor @MathLover1 very high - she rarely makes mistakes.


But even first class tutor is not guaranteed of making mistakes - sometimes :)