Whether the statement “When performing the division frac{x^{5} +1}{x + 1} there's no need for me to follow all the steps involved in polynomial long division because I can work the problem in my head and see that the quotient must be x^{4} + 1 ”makes sense or not.” Makes sense or not.

Whether the statement “When performing the division $\frac{{x}^{5}+1}{x+1}$ there's no need for me to follow all the steps involved in polynomial long division because I can work the problem in my head and see that the quotient must be ${x}^{4}+1$ ”makes sense or not.” Makes sense or not.
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svartmaleJ
No, the statement doesn't make sense as all the steps involved in polynomial long division are to be followed irrespective of the degree of the divisor and the dividend. Considering $\left({x}^{4}+1\right)$ as the quotient without solving the question reflects a misconception.
The statement doesn't make sense as all the steps of polynomial long division are to be followed properly.