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

Math
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.
3×25x+312×535×4+31×311×2+4x6
Divide the highest order term in the dividend 12×5 by the highest order term in divisor 3×2.
4×3
3×25x+312×535×4+31×311×2+4x6
Multiply the new quotient term by the divisor.
4×3
3×25x+312×535×4+31×311×2+4x6
+12×520×4+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
3×25x+312×535×4+31×311×2+4x6
12×5+20×412×3
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
4×3
3×25x+312×535×4+31×311×2+4x6
12×5+20×412×3
15×4+19×3
Pull the next terms from the original dividend down into the current dividend.
4×3
3×25x+312×535×4+31×311×2+4x6
12×5+20×412×3
15×4+19×311×2
Divide the highest order term in the dividend -15×4 by the highest order term in divisor 3×2.
4×35×2
3×25x+312×535×4+31×311×2+4x6
12×5+20×412×3
15×4+19×311×2
Multiply the new quotient term by the divisor.
4×35×2
3×25x+312×535×4+31×311×2+4x6
12×5+20×412×3
15×4+19×311×2
15×4+25×315×2
The expression needs to be subtracted from the dividend, so change all the signs in -15×4+25×3-15×2
4×35×2
3×25x+312×535×4+31×311×2+4x6
12×5+20×412×3
15×4+19×311×2
+15×425×3+15×2
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
4×35×2
3×25x+312×535×4+31×311×2+4x6
12×5+20×412×3
15×4+19×311×2
+15×425×3+15×2
6×3+4×2
Pull the next terms from the original dividend down into the current dividend.
4×35×2
3×25x+312×535×4+31×311×2+4x6
12×5+20×412×3
15×4+19×311×2
+15×425×3+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.
4×35×22x
3×25x+312×535×4+31×311×2+4x6
12×5+20×412×3
15×4+19×311×2
+15×425×3+15×2
6×3+4×2+4x
Multiply the new quotient term by the divisor.
4×35×22x
3×25x+312×535×4+31×311×2+4x6
12×5+20×412×3
15×4+19×311×2
+15×425×3+15×2
6×3+4×2+4x
6×3+10×26x
The expression needs to be subtracted from the dividend, so change all the signs in -6×3+10×2-6x
4×35×22x
3×25x+312×535×4+31×311×2+4x6
12×5+20×412×3
15×4+19×311×2
+15×425×3+15×2
6×3+4×2+4x
+6×310×2+6x
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
4×35×22x
3×25x+312×535×4+31×311×2+4x6
12×5+20×412×3
15×4+19×311×2
+15×425×3+15×2
6×3+4×2+4x
+6×310×2+6x
6×2+10x
Pull the next terms from the original dividend down into the current dividend.
4×35×22x
3×25x+312×535×4+31×311×2+4x6
12×5+20×412×3
15×4+19×311×2
+15×425×3+15×2
6×3+4×2+4x
+6×310×2+6x
6×2+10x6
Divide the highest order term in the dividend -6×2 by the highest order term in divisor 3×2.
4×35×22x2
3×25x+312×535×4+31×311×2+4x6
12×5+20×412×3
15×4+19×311×2
+15×425×3+15×2
6×3+4×2+4x
+6×310×2+6x
6×2+10x6
Multiply the new quotient term by the divisor.
4×35×22x2
3×25x+312×535×4+31×311×2+4x6
12×5+20×412×3
15×4+19×311×2
+15×425×3+15×2
6×3+4×2+4x
+6×310×2+6x
6×2+10x6
6×2+10x6
The expression needs to be subtracted from the dividend, so change all the signs in -6×2+10x-6
4×35×22x2
3×25x+312×535×4+31×311×2+4x6
12×5+20×412×3
15×4+19×311×2
+15×425×3+15×2
6×3+4×2+4x
+6×310×2+6x
6×2+10x6
+6×210x+6
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
4×35×22x2
3×25x+312×535×4+31×311×2+4x6
12×5+20×412×3
15×4+19×311×2
+15×425×3+15×2
6×3+4×2+4x
+6×310×2+6x
6×2+10x6
+6×210x+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)

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