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

Problem

(x4−3*x3+6*x2−3*x+5)/(x2+1)

Solution

1. Set up the polynomial long division by dividing the leading term of the dividend x4 by the leading term of the divisor x2

x4/x2=x2

2. Multiply the divisor x2+1 by x2 and subtract the result from the dividend.

(x4−3*x3+6*x2−3*x+5)−(x4+x2)=−3*x3+5*x2−3*x+5

3. Divide the new leading term −3*x3 by x2

−3*x3/x2=−3*x

4. Multiply the divisor x2+1 by −3*x and subtract from the current remainder.

(−3*x3+5*x2−3*x+5)−(−3*x3−3*x)=5*x2+5

5. Divide the new leading term 5*x2 by x2

5*x2/x2=5

6. Multiply the divisor x2+1 by 5 and subtract from the current remainder.

(5*x2+5)−(5*x2+5)=0

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

x2−3*x+5

Final Answer

(x4−3*x3+6*x2−3*x+5)/(x2+1)=x2−3*x+5

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