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

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 + 1 3×5 + 0x4 + 14×3 + 13×2 – 12x + 13
Divide the highest order term in the dividend 3×5 by the highest order term in divisor x2.
 3×3 x2 + 0x + 1 3×5 + 0x4 + 14×3 + 13×2 – 12x + 13
Multiply the new quotient term by the divisor.
 3×3 x2 + 0x + 1 3×5 + 0x4 + 14×3 + 13×2 – 12x + 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 + 1 3×5 + 0x4 + 14×3 + 13×2 – 12x + 13 – 3×5 – 0 – 3×3
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 3×3 x2 + 0x + 1 3×5 + 0x4 + 14×3 + 13×2 – 12x + 13 – 3×5 – 0 – 3×3 + 11×3
Pull the next term from the original dividend down into the current dividend.
 3×3 x2 + 0x + 1 3×5 + 0x4 + 14×3 + 13×2 – 12x + 13 – 3×5 – 0 – 3×3 + 11×3 + 13×2 – 12x
Divide the highest order term in the dividend 11×3 by the highest order term in divisor x2.
 3×3 + 0x2 + 11x x2 + 0x + 1 3×5 + 0x4 + 14×3 + 13×2 – 12x + 13 – 3×5 – 0 – 3×3 + 11×3 + 13×2 – 12x
Multiply the new quotient term by the divisor.
 3×3 + 0x2 + 11x x2 + 0x + 1 3×5 + 0x4 + 14×3 + 13×2 – 12x + 13 – 3×5 – 0 – 3×3 + 11×3 + 13×2 – 12x + 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 + 1 3×5 + 0x4 + 14×3 + 13×2 – 12x + 13 – 3×5 – 0 – 3×3 + 11×3 + 13×2 – 12x – 11×3 – 0 – 11x
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 3×3 + 0x2 + 11x x2 + 0x + 1 3×5 + 0x4 + 14×3 + 13×2 – 12x + 13 – 3×5 – 0 – 3×3 + 11×3 + 13×2 – 12x – 11×3 – 0 – 11x + 13×2 – 23x
Pull the next terms from the original dividend down into the current dividend.
 3×3 + 0x2 + 11x x2 + 0x + 1 3×5 + 0x4 + 14×3 + 13×2 – 12x + 13 – 3×5 – 0 – 3×3 + 11×3 + 13×2 – 12x – 11×3 – 0 – 11x + 13×2 – 23x + 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 + 1 3×5 + 0x4 + 14×3 + 13×2 – 12x + 13 – 3×5 – 0 – 3×3 + 11×3 + 13×2 – 12x – 11×3 – 0 – 11x + 13×2 – 23x + 13
Multiply the new quotient term by the divisor.
 3×3 + 0x2 + 11x + 13 x2 + 0x + 1 3×5 + 0x4 + 14×3 + 13×2 – 12x + 13 – 3×5 – 0 – 3×3 + 11×3 + 13×2 – 12x – 11×3 – 0 – 11x + 13×2 – 23x + 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 + 1 3×5 + 0x4 + 14×3 + 13×2 – 12x + 13 – 3×5 – 0 – 3×3 + 11×3 + 13×2 – 12x – 11×3 – 0 – 11x + 13×2 – 23x + 13 – 13×2 – 0 – 13
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 3×3 + 0x2 + 11x + 13 x2 + 0x + 1 3×5 + 0x4 + 14×3 + 13×2 – 12x + 13 – 3×5 – 0 – 3×3 + 11×3 + 13×2 – 12x – 11×3 – 0 – 11x + 13×2 – 23x + 13 – 13×2 – 0 – 13 – 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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