Question

Can x^{​​​​​​2}​​​​​-1 be the quotient on division of x^{​​​​​​6} + 2x³ + x-1​​​​x-1by a polynomial in x of degree 5?

Answer 1

No (x2-1) cannot be the quotient on division of x6-2x3+x-1 by a polynomial in x of degree 5 because the degree of product of the quotient and divisor should be equal to power of dividend.

So here the degree of product of quotient and divisor is 7.

But the degree of x6-2x3+x-1 is 6.

Hope it helps
All the best.