Divide (x^4-3x^3+6x^2-3x+5)/(x^2+1)

Problem

(x^4−3*x^3+6*x^2−3*x+5)/(x^2+1)

Solution

1. Set up the polynomial long division by dividing the leading term of the dividend x^4 by the leading term of the divisor x^2

x^4/x^2=x^2

2. Multiply the divisor x^2+1 by x^2 and subtract the result from the dividend.

(x^4−3*x^3+6*x^2−3*x+5)−(x^4+x^2)=−3*x^3+5*x^2−3*x+5

3. Divide the new leading term −3*x^3 by x^2

−3*x^3/x^2=−3*x

4. Multiply the divisor x^2+1 by −3*x and subtract from the current remainder.

(−3*x^3+5*x^2−3*x+5)−(−3*x^3−3*x)=5*x^2+5

5. Divide the new leading term 5*x^2 by x^2

5*x^2/x^2=5

6. Multiply the divisor x^2+1 by 5 and subtract from the current remainder.

(5*x^2+5)−(5*x^2+5)=0

7. Combine the quotient terms found in steps 1, 3, and 5.

x^2−3*x+5

Final Answer

(x^4−3*x^3+6*x^2−3*x+5)/(x^2+1)=x^2−3*x+5

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