# Divide (z^2-27)/(z-3)

z2-27z-3
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of 0.
 z – 3 z2 + 0z – 27
Divide the highest order term in the dividend z2 by the highest order term in divisor z.
 z z – 3 z2 + 0z – 27
Multiply the new quotient term by the divisor.
 z z – 3 z2 + 0z – 27 + z2 – 3z
The expression needs to be subtracted from the dividend, so change all the signs in z2-3z
 z z – 3 z2 + 0z – 27 – z2 + 3z
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 z z – 3 z2 + 0z – 27 – z2 + 3z + 3z
Pull the next terms from the original dividend down into the current dividend.
 z z – 3 z2 + 0z – 27 – z2 + 3z + 3z – 27
Divide the highest order term in the dividend 3z by the highest order term in divisor z.
 z + 3 z – 3 z2 + 0z – 27 – z2 + 3z + 3z – 27
Multiply the new quotient term by the divisor.
 z + 3 z – 3 z2 + 0z – 27 – z2 + 3z + 3z – 27 + 3z – 9
The expression needs to be subtracted from the dividend, so change all the signs in 3z-9
 z + 3 z – 3 z2 + 0z – 27 – z2 + 3z + 3z – 27 – 3z + 9
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 z + 3 z – 3 z2 + 0z – 27 – z2 + 3z + 3z – 27 – 3z + 9 – 18
The final answer is the quotient plus the remainder over the divisor.
z+3-18z-3
Divide (z^2-27)/(z-3)