Divide Using Long Polynomial Division (6x^3+10x^2+x+8)/(2x^2+1)

Problem

(6*x3+10*x2+x+8)/(2*x2+1)

Solution

1. Set up the long division by placing the dividend 6*x3+10*x2+x+8 inside the division bracket and the divisor 2*x2+1 outside.

2. Divide the first term of the dividend 6*x3 by the first term of the divisor 2*x2 to get the first term of the quotient.

(6*x3)/(2*x2)=3*x

3. Multiply the entire divisor 2*x2+1 by 3*x and subtract the result from the dividend.

3*x*(2*x2+1)=6*x3+3*x

(6*x3+10*x2+x+8)−(6*x3+3*x)=10*x2−2*x+8

4. Divide the first term of the new polynomial 10*x2 by the first term of the divisor 2*x2 to get the next term of the quotient.

(10*x2)/(2*x2)=5

5. Multiply the divisor 2*x2+1 by 5 and subtract from the current polynomial to find the remainder.

5*(2*x2+1)=10*x2+5

(10*x2−2*x+8)−(10*x2+5)=−2*x+3

6. Write the final result as the quotient plus the remainder over the divisor.

Final Answer

(6*x3+10*x2+x+8)/(2*x2+1)=3*x+5+(−2*x+3)/(2*x2+1)

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