Divide Using Long Polynomial Division (x^3-9)/(x^2+1)

Problem

(x^3−9)÷(x^2+1)

Solution

1. Set up the long division by writing the dividend x^3+0*x^2+0*x−9 and the divisor x^2+1 including placeholder terms for missing powers of x

2. Divide the leading term of the dividend x^3 by the leading term of the divisor x^2 to get the first term of the quotient, x

3. Multiply the divisor x^2+1 by the quotient term x to get x^3+x

4. Subtract this result from the dividend: (x^3+0*x^2+0*x)−(x^3+x)=−x

5. Bring down the remaining constant −9 to get the new remainder −x−9

6. Identify that the degree of the remainder −x−9 is less than the degree of the divisor x^2+1 so the division is complete.

7. Write the final result in the form quotient+remainder/divisor

Final Answer

(x^3−9)/(x^2+1)=x+(−x−9)/(x^2+1)

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