# Divide (n^2+6n+8)/(n+3)

n2+6n+8n+3
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of 0.
 n + 3 n2 + 6n + 8
Divide the highest order term in the dividend n2 by the highest order term in divisor n.
 n n + 3 n2 + 6n + 8
Multiply the new quotient term by the divisor.
 n n + 3 n2 + 6n + 8 + n2 + 3n
The expression needs to be subtracted from the dividend, so change all the signs in n2+3n
 n n + 3 n2 + 6n + 8 – n2 – 3n
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 n n + 3 n2 + 6n + 8 – n2 – 3n + 3n
Pull the next terms from the original dividend down into the current dividend.
 n n + 3 n2 + 6n + 8 – n2 – 3n + 3n + 8
Divide the highest order term in the dividend 3n by the highest order term in divisor n.
 n + 3 n + 3 n2 + 6n + 8 – n2 – 3n + 3n + 8
Multiply the new quotient term by the divisor.
 n + 3 n + 3 n2 + 6n + 8 – n2 – 3n + 3n + 8 + 3n + 9
The expression needs to be subtracted from the dividend, so change all the signs in 3n+9
 n + 3 n + 3 n2 + 6n + 8 – n2 – 3n + 3n + 8 – 3n – 9
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 n + 3 n + 3 n2 + 6n + 8 – n2 – 3n + 3n + 8 – 3n – 9 – 1
The final answer is the quotient plus the remainder over the divisor.
n+3-1n+3
Divide (n^2+6n+8)/(n+3)