# Divide (6r^3-9r^2-19r-24)/(r-3)

6r3-9r2-19r-24r-3
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of 0.
 r – 3 6r3 – 9r2 – 19r – 24
Divide the highest order term in the dividend 6r3 by the highest order term in divisor r.
 6r2 r – 3 6r3 – 9r2 – 19r – 24
Multiply the new quotient term by the divisor.
 6r2 r – 3 6r3 – 9r2 – 19r – 24 + 6r3 – 18r2
The expression needs to be subtracted from the dividend, so change all the signs in 6r3-18r2
 6r2 r – 3 6r3 – 9r2 – 19r – 24 – 6r3 + 18r2
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 6r2 r – 3 6r3 – 9r2 – 19r – 24 – 6r3 + 18r2 + 9r2
Pull the next terms from the original dividend down into the current dividend.
 6r2 r – 3 6r3 – 9r2 – 19r – 24 – 6r3 + 18r2 + 9r2 – 19r
Divide the highest order term in the dividend 9r2 by the highest order term in divisor r.
 6r2 + 9r r – 3 6r3 – 9r2 – 19r – 24 – 6r3 + 18r2 + 9r2 – 19r
Multiply the new quotient term by the divisor.
 6r2 + 9r r – 3 6r3 – 9r2 – 19r – 24 – 6r3 + 18r2 + 9r2 – 19r + 9r2 – 27r
The expression needs to be subtracted from the dividend, so change all the signs in 9r2-27r
 6r2 + 9r r – 3 6r3 – 9r2 – 19r – 24 – 6r3 + 18r2 + 9r2 – 19r – 9r2 + 27r
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 6r2 + 9r r – 3 6r3 – 9r2 – 19r – 24 – 6r3 + 18r2 + 9r2 – 19r – 9r2 + 27r + 8r
Pull the next terms from the original dividend down into the current dividend.
 6r2 + 9r r – 3 6r3 – 9r2 – 19r – 24 – 6r3 + 18r2 + 9r2 – 19r – 9r2 + 27r + 8r – 24
Divide the highest order term in the dividend 8r by the highest order term in divisor r.
 6r2 + 9r + 8 r – 3 6r3 – 9r2 – 19r – 24 – 6r3 + 18r2 + 9r2 – 19r – 9r2 + 27r + 8r – 24
Multiply the new quotient term by the divisor.
 6r2 + 9r + 8 r – 3 6r3 – 9r2 – 19r – 24 – 6r3 + 18r2 + 9r2 – 19r – 9r2 + 27r + 8r – 24 + 8r – 24
The expression needs to be subtracted from the dividend, so change all the signs in 8r-24
 6r2 + 9r + 8 r – 3 6r3 – 9r2 – 19r – 24 – 6r3 + 18r2 + 9r2 – 19r – 9r2 + 27r + 8r – 24 – 8r + 24
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 6r2 + 9r + 8 r – 3 6r3 – 9r2 – 19r – 24 – 6r3 + 18r2 + 9r2 – 19r – 9r2 + 27r + 8r – 24 – 8r + 24 0
Since the remander is 0, the final answer is the quotient.
6r2+9r+8
Divide (6r^3-9r^2-19r-24)/(r-3)