4) 7 x^3+x^2+x div x^2+1 Long division

To perform long division on the given polynomial divided by , we follow these steps:1. **Divide the leading term of the dividend by the leading term of the divisor:** 2. **Multiply the entire divisor by this result and subtract from the original polynomial:** 3. **Repeat the process with the new polynomial :** 4. **Since the degree of the remainder is less than the degree of the divisor , we stop here.**So, the quotient is and the remainder is .Thus, the result of the division is: Or, more neatly written: