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

3×5+15×3-4+11×2+7×4+8×2+x2+x
Expand 3×5+15×3-4+11×2+7×4+8x.
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.
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 + 2 3×5 + 7×4 + 15×3 + 11×2 + 8x – 4
Divide the highest order term in the dividend 3×5 by the highest order term in divisor x2.
 3×3 x2 + x + 2 3×5 + 7×4 + 15×3 + 11×2 + 8x – 4
Multiply the new quotient term by the divisor.
 3×3 x2 + x + 2 3×5 + 7×4 + 15×3 + 11×2 + 8x – 4 + 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 + 2 3×5 + 7×4 + 15×3 + 11×2 + 8x – 4 – 3×5 – 3×4 – 6×3
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 3×3 x2 + x + 2 3×5 + 7×4 + 15×3 + 11×2 + 8x – 4 – 3×5 – 3×4 – 6×3 + 4×4 + 9×3
Pull the next terms from the original dividend down into the current dividend.
 3×3 x2 + x + 2 3×5 + 7×4 + 15×3 + 11×2 + 8x – 4 – 3×5 – 3×4 – 6×3 + 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 + 2 3×5 + 7×4 + 15×3 + 11×2 + 8x – 4 – 3×5 – 3×4 – 6×3 + 4×4 + 9×3 + 11×2
Multiply the new quotient term by the divisor.
 3×3 + 4×2 x2 + x + 2 3×5 + 7×4 + 15×3 + 11×2 + 8x – 4 – 3×5 – 3×4 – 6×3 + 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 + 2 3×5 + 7×4 + 15×3 + 11×2 + 8x – 4 – 3×5 – 3×4 – 6×3 + 4×4 + 9×3 + 11×2 – 4×4 – 4×3 – 8×2
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 3×3 + 4×2 x2 + x + 2 3×5 + 7×4 + 15×3 + 11×2 + 8x – 4 – 3×5 – 3×4 – 6×3 + 4×4 + 9×3 + 11×2 – 4×4 – 4×3 – 8×2 + 5×3 + 3×2
Pull the next terms from the original dividend down into the current dividend.
 3×3 + 4×2 x2 + x + 2 3×5 + 7×4 + 15×3 + 11×2 + 8x – 4 – 3×5 – 3×4 – 6×3 + 4×4 + 9×3 + 11×2 – 4×4 – 4×3 – 8×2 + 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 + 2 3×5 + 7×4 + 15×3 + 11×2 + 8x – 4 – 3×5 – 3×4 – 6×3 + 4×4 + 9×3 + 11×2 – 4×4 – 4×3 – 8×2 + 5×3 + 3×2 + 8x
Multiply the new quotient term by the divisor.
 3×3 + 4×2 + 5x x2 + x + 2 3×5 + 7×4 + 15×3 + 11×2 + 8x – 4 – 3×5 – 3×4 – 6×3 + 4×4 + 9×3 + 11×2 – 4×4 – 4×3 – 8×2 + 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 + 2 3×5 + 7×4 + 15×3 + 11×2 + 8x – 4 – 3×5 – 3×4 – 6×3 + 4×4 + 9×3 + 11×2 – 4×4 – 4×3 – 8×2 + 5×3 + 3×2 + 8x – 5×3 – 5×2 – 10x
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 3×3 + 4×2 + 5x x2 + x + 2 3×5 + 7×4 + 15×3 + 11×2 + 8x – 4 – 3×5 – 3×4 – 6×3 + 4×4 + 9×3 + 11×2 – 4×4 – 4×3 – 8×2 + 5×3 + 3×2 + 8x – 5×3 – 5×2 – 10x – 2×2 – 2x
Pull the next terms from the original dividend down into the current dividend.
 3×3 + 4×2 + 5x x2 + x + 2 3×5 + 7×4 + 15×3 + 11×2 + 8x – 4 – 3×5 – 3×4 – 6×3 + 4×4 + 9×3 + 11×2 – 4×4 – 4×3 – 8×2 + 5×3 + 3×2 + 8x – 5×3 – 5×2 – 10x – 2×2 – 2x – 4
Divide the highest order term in the dividend -2×2 by the highest order term in divisor x2.
 3×3 + 4×2 + 5x – 2 x2 + x + 2 3×5 + 7×4 + 15×3 + 11×2 + 8x – 4 – 3×5 – 3×4 – 6×3 + 4×4 + 9×3 + 11×2 – 4×4 – 4×3 – 8×2 + 5×3 + 3×2 + 8x – 5×3 – 5×2 – 10x – 2×2 – 2x – 4
Multiply the new quotient term by the divisor.
 3×3 + 4×2 + 5x – 2 x2 + x + 2 3×5 + 7×4 + 15×3 + 11×2 + 8x – 4 – 3×5 – 3×4 – 6×3 + 4×4 + 9×3 + 11×2 – 4×4 – 4×3 – 8×2 + 5×3 + 3×2 + 8x – 5×3 – 5×2 – 10x – 2×2 – 2x – 4 – 2×2 – 2x – 4
The expression needs to be subtracted from the dividend, so change all the signs in -2×2-2x-4
 3×3 + 4×2 + 5x – 2 x2 + x + 2 3×5 + 7×4 + 15×3 + 11×2 + 8x – 4 – 3×5 – 3×4 – 6×3 + 4×4 + 9×3 + 11×2 – 4×4 – 4×3 – 8×2 + 5×3 + 3×2 + 8x – 5×3 – 5×2 – 10x – 2×2 – 2x – 4 + 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 + 5x – 2 x2 + x + 2 3×5 + 7×4 + 15×3 + 11×2 + 8x – 4 – 3×5 – 3×4 – 6×3 + 4×4 + 9×3 + 11×2 – 4×4 – 4×3 – 8×2 + 5×3 + 3×2 + 8x – 5×3 – 5×2 – 10x – 2×2 – 2x – 4 + 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)