Question

Can $(x^2-1)$ be the quotient on division of $x^6+2x^3+x-1$ by a polynomial in $x$ of degree 5?

Answer 1

No, $x^2-1$ cannot be the quotient on division of $x^6-2x^3+x-1$ by a

polynomial in degree $5$ because the degree of the product of the

quotient and the divisor should be equal to the power of the dividend.

Here, the degree of the product of the quotient and the divisor is $7$. But the degree of $x^6-2x^3+x-1$ is $6$