# Divide (y^3-y^2-8y+3)÷(y+2)

(y3-y2-8y+3)÷(y+2)
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of 0.
 y + 2 y3 – y2 – 8y + 3
Divide the highest order term in the dividend y3 by the highest order term in divisor y.
 y2 y + 2 y3 – y2 – 8y + 3
Multiply the new quotient term by the divisor.
 y2 y + 2 y3 – y2 – 8y + 3 + y3 + 2y2
The expression needs to be subtracted from the dividend, so change all the signs in y3+2y2
 y2 y + 2 y3 – y2 – 8y + 3 – y3 – 2y2
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 y2 y + 2 y3 – y2 – 8y + 3 – y3 – 2y2 – 3y2
Pull the next terms from the original dividend down into the current dividend.
 y2 y + 2 y3 – y2 – 8y + 3 – y3 – 2y2 – 3y2 – 8y
Divide the highest order term in the dividend -3y2 by the highest order term in divisor y.
 y2 – 3y y + 2 y3 – y2 – 8y + 3 – y3 – 2y2 – 3y2 – 8y
Multiply the new quotient term by the divisor.
 y2 – 3y y + 2 y3 – y2 – 8y + 3 – y3 – 2y2 – 3y2 – 8y – 3y2 – 6y
The expression needs to be subtracted from the dividend, so change all the signs in -3y2-6y
 y2 – 3y y + 2 y3 – y2 – 8y + 3 – y3 – 2y2 – 3y2 – 8y + 3y2 + 6y
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 y2 – 3y y + 2 y3 – y2 – 8y + 3 – y3 – 2y2 – 3y2 – 8y + 3y2 + 6y – 2y
Pull the next terms from the original dividend down into the current dividend.
 y2 – 3y y + 2 y3 – y2 – 8y + 3 – y3 – 2y2 – 3y2 – 8y + 3y2 + 6y – 2y + 3
Divide the highest order term in the dividend -2y by the highest order term in divisor y.
 y2 – 3y – 2 y + 2 y3 – y2 – 8y + 3 – y3 – 2y2 – 3y2 – 8y + 3y2 + 6y – 2y + 3
Multiply the new quotient term by the divisor.
 y2 – 3y – 2 y + 2 y3 – y2 – 8y + 3 – y3 – 2y2 – 3y2 – 8y + 3y2 + 6y – 2y + 3 – 2y – 4
The expression needs to be subtracted from the dividend, so change all the signs in -2y-4
 y2 – 3y – 2 y + 2 y3 – y2 – 8y + 3 – y3 – 2y2 – 3y2 – 8y + 3y2 + 6y – 2y + 3 + 2y + 4
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 y2 – 3y – 2 y + 2 y3 – y2 – 8y + 3 – y3 – 2y2 – 3y2 – 8y + 3y2 + 6y – 2y + 3 + 2y + 4 + 7
The final answer is the quotient plus the remainder over the divisor.
y2-3y-2+7y+2
Divide (y^3-y^2-8y+3)÷(y+2)