Divide (3x^5+14x^3+13x^2-12x+13)/(x^2+1)

Math
3×5+14×3+13×2-12x+13×2+1
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of 0.
x2+0x+13×5+0x4+14×3+13×212x+13
Divide the highest order term in the dividend 3×5 by the highest order term in divisor x2.
3×3
x2+0x+13×5+0x4+14×3+13×212x+13
Multiply the new quotient term by the divisor.
3×3
x2+0x+13×5+0x4+14×3+13×212x+13
+3×5+0+3×3
The expression needs to be subtracted from the dividend, so change all the signs in 3×5+0+3×3
3×3
x2+0x+13×5+0x4+14×3+13×212x+13
3×503×3
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
3×3
x2+0x+13×5+0x4+14×3+13×212x+13
3×503×3
+11×3
Pull the next term from the original dividend down into the current dividend.
3×3
x2+0x+13×5+0x4+14×3+13×212x+13
3×503×3
+11×3+13×212x
Divide the highest order term in the dividend 11×3 by the highest order term in divisor x2.
3×3+0x2+11x
x2+0x+13×5+0x4+14×3+13×212x+13
3×503×3
+11×3+13×212x
Multiply the new quotient term by the divisor.
3×3+0x2+11x
x2+0x+13×5+0x4+14×3+13×212x+13
3×503×3
+11×3+13×212x
+11×3+0+11x
The expression needs to be subtracted from the dividend, so change all the signs in 11×3+0+11x
3×3+0x2+11x
x2+0x+13×5+0x4+14×3+13×212x+13
3×503×3
+11×3+13×212x
11×3011x
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
3×3+0x2+11x
x2+0x+13×5+0x4+14×3+13×212x+13
3×503×3
+11×3+13×212x
11×3011x
+13×223x
Pull the next terms from the original dividend down into the current dividend.
3×3+0x2+11x
x2+0x+13×5+0x4+14×3+13×212x+13
3×503×3
+11×3+13×212x
11×3011x
+13×223x+13
Divide the highest order term in the dividend 13×2 by the highest order term in divisor x2.
3×3+0x2+11x+13
x2+0x+13×5+0x4+14×3+13×212x+13
3×503×3
+11×3+13×212x
11×3011x
+13×223x+13
Multiply the new quotient term by the divisor.
3×3+0x2+11x+13
x2+0x+13×5+0x4+14×3+13×212x+13
3×503×3
+11×3+13×212x
11×3011x
+13×223x+13
+13×2+0+13
The expression needs to be subtracted from the dividend, so change all the signs in 13×2+0+13
3×3+0x2+11x+13
x2+0x+13×5+0x4+14×3+13×212x+13
3×503×3
+11×3+13×212x
11×3011x
+13×223x+13
13×2013
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
3×3+0x2+11x+13
x2+0x+13×5+0x4+14×3+13×212x+13
3×503×3
+11×3+13×212x
11×3011x
+13×223x+13
13×2013
23x+0
The final answer is the quotient plus the remainder over the divisor.
3×3+11x+13+-23xx2+1
Divide (3x^5+14x^3+13x^2-12x+13)/(x^2+1)

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