# Divide (12x^4+17x^3+8x-40)÷(x+2)

(12×4+17×3+8x-40)÷(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.
 x + 2 12×4 + 17×3 + 0x2 + 8x – 40
Divide the highest order term in the dividend 12×4 by the highest order term in divisor x.
 12×3 x + 2 12×4 + 17×3 + 0x2 + 8x – 40
Multiply the new quotient term by the divisor.
 12×3 x + 2 12×4 + 17×3 + 0x2 + 8x – 40 + 12×4 + 24×3
The expression needs to be subtracted from the dividend, so change all the signs in 12×4+24×3
 12×3 x + 2 12×4 + 17×3 + 0x2 + 8x – 40 – 12×4 – 24×3
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 12×3 x + 2 12×4 + 17×3 + 0x2 + 8x – 40 – 12×4 – 24×3 – 7×3
Pull the next terms from the original dividend down into the current dividend.
 12×3 x + 2 12×4 + 17×3 + 0x2 + 8x – 40 – 12×4 – 24×3 – 7×3 + 0x2
Divide the highest order term in the dividend -7×3 by the highest order term in divisor x.
 12×3 – 7×2 x + 2 12×4 + 17×3 + 0x2 + 8x – 40 – 12×4 – 24×3 – 7×3 + 0x2
Multiply the new quotient term by the divisor.
 12×3 – 7×2 x + 2 12×4 + 17×3 + 0x2 + 8x – 40 – 12×4 – 24×3 – 7×3 + 0x2 – 7×3 – 14×2
The expression needs to be subtracted from the dividend, so change all the signs in -7×3-14×2
 12×3 – 7×2 x + 2 12×4 + 17×3 + 0x2 + 8x – 40 – 12×4 – 24×3 – 7×3 + 0x2 + 7×3 + 14×2
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 12×3 – 7×2 x + 2 12×4 + 17×3 + 0x2 + 8x – 40 – 12×4 – 24×3 – 7×3 + 0x2 + 7×3 + 14×2 + 14×2
Pull the next terms from the original dividend down into the current dividend.
 12×3 – 7×2 x + 2 12×4 + 17×3 + 0x2 + 8x – 40 – 12×4 – 24×3 – 7×3 + 0x2 + 7×3 + 14×2 + 14×2 + 8x
Divide the highest order term in the dividend 14×2 by the highest order term in divisor x.
 12×3 – 7×2 + 14x x + 2 12×4 + 17×3 + 0x2 + 8x – 40 – 12×4 – 24×3 – 7×3 + 0x2 + 7×3 + 14×2 + 14×2 + 8x
Multiply the new quotient term by the divisor.
 12×3 – 7×2 + 14x x + 2 12×4 + 17×3 + 0x2 + 8x – 40 – 12×4 – 24×3 – 7×3 + 0x2 + 7×3 + 14×2 + 14×2 + 8x + 14×2 + 28x
The expression needs to be subtracted from the dividend, so change all the signs in 14×2+28x
 12×3 – 7×2 + 14x x + 2 12×4 + 17×3 + 0x2 + 8x – 40 – 12×4 – 24×3 – 7×3 + 0x2 + 7×3 + 14×2 + 14×2 + 8x – 14×2 – 28x
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 12×3 – 7×2 + 14x x + 2 12×4 + 17×3 + 0x2 + 8x – 40 – 12×4 – 24×3 – 7×3 + 0x2 + 7×3 + 14×2 + 14×2 + 8x – 14×2 – 28x – 20x
Pull the next terms from the original dividend down into the current dividend.
 12×3 – 7×2 + 14x x + 2 12×4 + 17×3 + 0x2 + 8x – 40 – 12×4 – 24×3 – 7×3 + 0x2 + 7×3 + 14×2 + 14×2 + 8x – 14×2 – 28x – 20x – 40
Divide the highest order term in the dividend -20x by the highest order term in divisor x.
 12×3 – 7×2 + 14x – 20 x + 2 12×4 + 17×3 + 0x2 + 8x – 40 – 12×4 – 24×3 – 7×3 + 0x2 + 7×3 + 14×2 + 14×2 + 8x – 14×2 – 28x – 20x – 40
Multiply the new quotient term by the divisor.
 12×3 – 7×2 + 14x – 20 x + 2 12×4 + 17×3 + 0x2 + 8x – 40 – 12×4 – 24×3 – 7×3 + 0x2 + 7×3 + 14×2 + 14×2 + 8x – 14×2 – 28x – 20x – 40 – 20x – 40
The expression needs to be subtracted from the dividend, so change all the signs in -20x-40
 12×3 – 7×2 + 14x – 20 x + 2 12×4 + 17×3 + 0x2 + 8x – 40 – 12×4 – 24×3 – 7×3 + 0x2 + 7×3 + 14×2 + 14×2 + 8x – 14×2 – 28x – 20x – 40 + 20x + 40
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 12×3 – 7×2 + 14x – 20 x + 2 12×4 + 17×3 + 0x2 + 8x – 40 – 12×4 – 24×3 – 7×3 + 0x2 + 7×3 + 14×2 + 14×2 + 8x – 14×2 – 28x – 20x – 40 + 20x + 40 0
Since the remander is 0, the final answer is the quotient.
12×3-7×2+14x-20
Divide (12x^4+17x^3+8x-40)÷(x+2)