Divide (x^5+7)/(x^3-1)

Problem

(x^5+7)/(x^3−1)

Solution

1. Set up the polynomial long division by dividing the leading term of the dividend x^5 by the leading term of the divisor x^3

2. Divide the first terms to get the first term of the quotient.

(x^5)/(x^3)=x^2

3. Multiply the divisor x^3−1 by the quotient term x^2

x^2*(x^3−1)=x^5−x^2

4. Subtract this result from the original dividend to find the new remainder.

(x^5+7)−(x^5−x^2)=x^2+7

5. Identify the final components since the degree of the remainder x^2+7 is less than the degree of the divisor x^3−1

6. Write the result in the form Quotient+Remainder/Divisor

Final Answer

(x^5+7)/(x^3−1)=x^2+(x^2+7)/(x^3−1)

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