Divide (3x^5+15x^3-4+11x^2+7x^4+8x)/(2+x^2+x)

Math
3×5+15×3-4+11×2+7×4+8×2+x2+x
Expand 3×5+15×3-4+11×2+7×4+8x.
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Move -4.
3×5+15×3+11×2-4+7×4+8×2+x2+x
Move -4.
3×5+15×3+11×2+7×4-4+8×2+x2+x
Move 11×2.
3×5+15×3+7×4+11×2-4+8×2+x2+x
Move 15×3.
3×5+7×4+15×3+11×2-4+8×2+x2+x
Move -4.
3×5+7×4+15×3+11×2+8x-42+x2+x
3×5+7×4+15×3+11×2+8x-42+x2+x
Expand 2+x2+x.
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Reorder 2 and x2.
3×5+7×4+15×3+11×2+8x-4×2+2+x
Move 2.
3×5+7×4+15×3+11×2+8x-4×2+x+2
3×5+7×4+15×3+11×2+8x-4×2+x+2
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of 0.
x2+x+23×5+7×4+15×3+11×2+8x4
Divide the highest order term in the dividend 3×5 by the highest order term in divisor x2.
3×3
x2+x+23×5+7×4+15×3+11×2+8x4
Multiply the new quotient term by the divisor.
3×3
x2+x+23×5+7×4+15×3+11×2+8x4
+3×5+3×4+6×3
The expression needs to be subtracted from the dividend, so change all the signs in 3×5+3×4+6×3
3×3
x2+x+23×5+7×4+15×3+11×2+8x4
3×53×46×3
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
3×3
x2+x+23×5+7×4+15×3+11×2+8x4
3×53×46×3
+4×4+9×3
Pull the next terms from the original dividend down into the current dividend.
3×3
x2+x+23×5+7×4+15×3+11×2+8x4
3×53×46×3
+4×4+9×3+11×2
Divide the highest order term in the dividend 4×4 by the highest order term in divisor x2.
3×3+4×2
x2+x+23×5+7×4+15×3+11×2+8x4
3×53×46×3
+4×4+9×3+11×2
Multiply the new quotient term by the divisor.
3×3+4×2
x2+x+23×5+7×4+15×3+11×2+8x4
3×53×46×3
+4×4+9×3+11×2
+4×4+4×3+8×2
The expression needs to be subtracted from the dividend, so change all the signs in 4×4+4×3+8×2
3×3+4×2
x2+x+23×5+7×4+15×3+11×2+8x4
3×53×46×3
+4×4+9×3+11×2
4×44×38×2
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
3×3+4×2
x2+x+23×5+7×4+15×3+11×2+8x4
3×53×46×3
+4×4+9×3+11×2
4×44×38×2
+5×3+3×2
Pull the next terms from the original dividend down into the current dividend.
3×3+4×2
x2+x+23×5+7×4+15×3+11×2+8x4
3×53×46×3
+4×4+9×3+11×2
4×44×38×2
+5×3+3×2+8x
Divide the highest order term in the dividend 5×3 by the highest order term in divisor x2.
3×3+4×2+5x
x2+x+23×5+7×4+15×3+11×2+8x4
3×53×46×3
+4×4+9×3+11×2
4×44×38×2
+5×3+3×2+8x
Multiply the new quotient term by the divisor.
3×3+4×2+5x
x2+x+23×5+7×4+15×3+11×2+8x4
3×53×46×3
+4×4+9×3+11×2
4×44×38×2
+5×3+3×2+8x
+5×3+5×2+10x
The expression needs to be subtracted from the dividend, so change all the signs in 5×3+5×2+10x
3×3+4×2+5x
x2+x+23×5+7×4+15×3+11×2+8x4
3×53×46×3
+4×4+9×3+11×2
4×44×38×2
+5×3+3×2+8x
5×35×210x
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
3×3+4×2+5x
x2+x+23×5+7×4+15×3+11×2+8x4
3×53×46×3
+4×4+9×3+11×2
4×44×38×2
+5×3+3×2+8x
5×35×210x
2×22x
Pull the next terms from the original dividend down into the current dividend.
3×3+4×2+5x
x2+x+23×5+7×4+15×3+11×2+8x4
3×53×46×3
+4×4+9×3+11×2
4×44×38×2
+5×3+3×2+8x
5×35×210x
2×22x4
Divide the highest order term in the dividend -2×2 by the highest order term in divisor x2.
3×3+4×2+5x2
x2+x+23×5+7×4+15×3+11×2+8x4
3×53×46×3
+4×4+9×3+11×2
4×44×38×2
+5×3+3×2+8x
5×35×210x
2×22x4
Multiply the new quotient term by the divisor.
3×3+4×2+5x2
x2+x+23×5+7×4+15×3+11×2+8x4
3×53×46×3
+4×4+9×3+11×2
4×44×38×2
+5×3+3×2+8x
5×35×210x
2×22x4
2×22x4
The expression needs to be subtracted from the dividend, so change all the signs in -2×2-2x-4
3×3+4×2+5x2
x2+x+23×5+7×4+15×3+11×2+8x4
3×53×46×3
+4×4+9×3+11×2
4×44×38×2
+5×3+3×2+8x
5×35×210x
2×22x4
+2×2+2x+4
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
3×3+4×2+5x2
x2+x+23×5+7×4+15×3+11×2+8x4
3×53×46×3
+4×4+9×3+11×2
4×44×38×2
+5×3+3×2+8x
5×35×210x
2×22x4
+2×2+2x+4
0
Since the remander is 0, the final answer is the quotient.
3×3+4×2+5x-2
Divide (3x^5+15x^3-4+11x^2+7x^4+8x)/(2+x^2+x)

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