# Divide (12x^5-35x^4+31x^3-11x^2+4x-6)/(3x^2-5x+3)

12×5-35×4+31×3-11×2+4x-63×2-5x+3
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of 0.
 3×2 – 5x + 3 12×5 – 35×4 + 31×3 – 11×2 + 4x – 6
Divide the highest order term in the dividend 12×5 by the highest order term in divisor 3×2.
 4×3 3×2 – 5x + 3 12×5 – 35×4 + 31×3 – 11×2 + 4x – 6
Multiply the new quotient term by the divisor.
 4×3 3×2 – 5x + 3 12×5 – 35×4 + 31×3 – 11×2 + 4x – 6 + 12×5 – 20×4 + 12×3
The expression needs to be subtracted from the dividend, so change all the signs in 12×5-20×4+12×3
 4×3 3×2 – 5x + 3 12×5 – 35×4 + 31×3 – 11×2 + 4x – 6 – 12×5 + 20×4 – 12×3
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 4×3 3×2 – 5x + 3 12×5 – 35×4 + 31×3 – 11×2 + 4x – 6 – 12×5 + 20×4 – 12×3 – 15×4 + 19×3
Pull the next terms from the original dividend down into the current dividend.
 4×3 3×2 – 5x + 3 12×5 – 35×4 + 31×3 – 11×2 + 4x – 6 – 12×5 + 20×4 – 12×3 – 15×4 + 19×3 – 11×2
Divide the highest order term in the dividend -15×4 by the highest order term in divisor 3×2.
 4×3 – 5×2 3×2 – 5x + 3 12×5 – 35×4 + 31×3 – 11×2 + 4x – 6 – 12×5 + 20×4 – 12×3 – 15×4 + 19×3 – 11×2
Multiply the new quotient term by the divisor.
 4×3 – 5×2 3×2 – 5x + 3 12×5 – 35×4 + 31×3 – 11×2 + 4x – 6 – 12×5 + 20×4 – 12×3 – 15×4 + 19×3 – 11×2 – 15×4 + 25×3 – 15×2
The expression needs to be subtracted from the dividend, so change all the signs in -15×4+25×3-15×2
 4×3 – 5×2 3×2 – 5x + 3 12×5 – 35×4 + 31×3 – 11×2 + 4x – 6 – 12×5 + 20×4 – 12×3 – 15×4 + 19×3 – 11×2 + 15×4 – 25×3 + 15×2
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 4×3 – 5×2 3×2 – 5x + 3 12×5 – 35×4 + 31×3 – 11×2 + 4x – 6 – 12×5 + 20×4 – 12×3 – 15×4 + 19×3 – 11×2 + 15×4 – 25×3 + 15×2 – 6×3 + 4×2
Pull the next terms from the original dividend down into the current dividend.
 4×3 – 5×2 3×2 – 5x + 3 12×5 – 35×4 + 31×3 – 11×2 + 4x – 6 – 12×5 + 20×4 – 12×3 – 15×4 + 19×3 – 11×2 + 15×4 – 25×3 + 15×2 – 6×3 + 4×2 + 4x
Divide the highest order term in the dividend -6×3 by the highest order term in divisor 3×2.
 4×3 – 5×2 – 2x 3×2 – 5x + 3 12×5 – 35×4 + 31×3 – 11×2 + 4x – 6 – 12×5 + 20×4 – 12×3 – 15×4 + 19×3 – 11×2 + 15×4 – 25×3 + 15×2 – 6×3 + 4×2 + 4x
Multiply the new quotient term by the divisor.
 4×3 – 5×2 – 2x 3×2 – 5x + 3 12×5 – 35×4 + 31×3 – 11×2 + 4x – 6 – 12×5 + 20×4 – 12×3 – 15×4 + 19×3 – 11×2 + 15×4 – 25×3 + 15×2 – 6×3 + 4×2 + 4x – 6×3 + 10×2 – 6x
The expression needs to be subtracted from the dividend, so change all the signs in -6×3+10×2-6x
 4×3 – 5×2 – 2x 3×2 – 5x + 3 12×5 – 35×4 + 31×3 – 11×2 + 4x – 6 – 12×5 + 20×4 – 12×3 – 15×4 + 19×3 – 11×2 + 15×4 – 25×3 + 15×2 – 6×3 + 4×2 + 4x + 6×3 – 10×2 + 6x
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 4×3 – 5×2 – 2x 3×2 – 5x + 3 12×5 – 35×4 + 31×3 – 11×2 + 4x – 6 – 12×5 + 20×4 – 12×3 – 15×4 + 19×3 – 11×2 + 15×4 – 25×3 + 15×2 – 6×3 + 4×2 + 4x + 6×3 – 10×2 + 6x – 6×2 + 10x
Pull the next terms from the original dividend down into the current dividend.
 4×3 – 5×2 – 2x 3×2 – 5x + 3 12×5 – 35×4 + 31×3 – 11×2 + 4x – 6 – 12×5 + 20×4 – 12×3 – 15×4 + 19×3 – 11×2 + 15×4 – 25×3 + 15×2 – 6×3 + 4×2 + 4x + 6×3 – 10×2 + 6x – 6×2 + 10x – 6
Divide the highest order term in the dividend -6×2 by the highest order term in divisor 3×2.
 4×3 – 5×2 – 2x – 2 3×2 – 5x + 3 12×5 – 35×4 + 31×3 – 11×2 + 4x – 6 – 12×5 + 20×4 – 12×3 – 15×4 + 19×3 – 11×2 + 15×4 – 25×3 + 15×2 – 6×3 + 4×2 + 4x + 6×3 – 10×2 + 6x – 6×2 + 10x – 6
Multiply the new quotient term by the divisor.
 4×3 – 5×2 – 2x – 2 3×2 – 5x + 3 12×5 – 35×4 + 31×3 – 11×2 + 4x – 6 – 12×5 + 20×4 – 12×3 – 15×4 + 19×3 – 11×2 + 15×4 – 25×3 + 15×2 – 6×3 + 4×2 + 4x + 6×3 – 10×2 + 6x – 6×2 + 10x – 6 – 6×2 + 10x – 6
The expression needs to be subtracted from the dividend, so change all the signs in -6×2+10x-6
 4×3 – 5×2 – 2x – 2 3×2 – 5x + 3 12×5 – 35×4 + 31×3 – 11×2 + 4x – 6 – 12×5 + 20×4 – 12×3 – 15×4 + 19×3 – 11×2 + 15×4 – 25×3 + 15×2 – 6×3 + 4×2 + 4x + 6×3 – 10×2 + 6x – 6×2 + 10x – 6 + 6×2 – 10x + 6
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 4×3 – 5×2 – 2x – 2 3×2 – 5x + 3 12×5 – 35×4 + 31×3 – 11×2 + 4x – 6 – 12×5 + 20×4 – 12×3 – 15×4 + 19×3 – 11×2 + 15×4 – 25×3 + 15×2 – 6×3 + 4×2 + 4x + 6×3 – 10×2 + 6x – 6×2 + 10x – 6 + 6×2 – 10x + 6 0
Since the remander is 0, the final answer is the quotient.
4×3-5×2-2x-2
Divide (12x^5-35x^4+31x^3-11x^2+4x-6)/(3x^2-5x+3)