# Divide (6c^4-12c^2+18c+19)/(6c+6)

6c4-12c2+18c+196c+6
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of 0.
 6c + 6 6c4 + 0c3 – 12c2 + 18c + 19
Divide the highest order term in the dividend 6c4 by the highest order term in divisor 6c.
 c3 6c + 6 6c4 + 0c3 – 12c2 + 18c + 19
Multiply the new quotient term by the divisor.
 c3 6c + 6 6c4 + 0c3 – 12c2 + 18c + 19 + 6c4 + 6c3
The expression needs to be subtracted from the dividend, so change all the signs in 6c4+6c3
 c3 6c + 6 6c4 + 0c3 – 12c2 + 18c + 19 – 6c4 – 6c3
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 c3 6c + 6 6c4 + 0c3 – 12c2 + 18c + 19 – 6c4 – 6c3 – 6c3
Pull the next terms from the original dividend down into the current dividend.
 c3 6c + 6 6c4 + 0c3 – 12c2 + 18c + 19 – 6c4 – 6c3 – 6c3 – 12c2
Divide the highest order term in the dividend -6c3 by the highest order term in divisor 6c.
 c3 – c2 6c + 6 6c4 + 0c3 – 12c2 + 18c + 19 – 6c4 – 6c3 – 6c3 – 12c2
Multiply the new quotient term by the divisor.
 c3 – c2 6c + 6 6c4 + 0c3 – 12c2 + 18c + 19 – 6c4 – 6c3 – 6c3 – 12c2 – 6c3 – 6c2
The expression needs to be subtracted from the dividend, so change all the signs in -6c3-6c2
 c3 – c2 6c + 6 6c4 + 0c3 – 12c2 + 18c + 19 – 6c4 – 6c3 – 6c3 – 12c2 + 6c3 + 6c2
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 c3 – c2 6c + 6 6c4 + 0c3 – 12c2 + 18c + 19 – 6c4 – 6c3 – 6c3 – 12c2 + 6c3 + 6c2 – 6c2
Pull the next terms from the original dividend down into the current dividend.
 c3 – c2 6c + 6 6c4 + 0c3 – 12c2 + 18c + 19 – 6c4 – 6c3 – 6c3 – 12c2 + 6c3 + 6c2 – 6c2 + 18c
Divide the highest order term in the dividend -6c2 by the highest order term in divisor 6c.
 c3 – c2 – c 6c + 6 6c4 + 0c3 – 12c2 + 18c + 19 – 6c4 – 6c3 – 6c3 – 12c2 + 6c3 + 6c2 – 6c2 + 18c
Multiply the new quotient term by the divisor.
 c3 – c2 – c 6c + 6 6c4 + 0c3 – 12c2 + 18c + 19 – 6c4 – 6c3 – 6c3 – 12c2 + 6c3 + 6c2 – 6c2 + 18c – 6c2 – 6c
The expression needs to be subtracted from the dividend, so change all the signs in -6c2-6c
 c3 – c2 – c 6c + 6 6c4 + 0c3 – 12c2 + 18c + 19 – 6c4 – 6c3 – 6c3 – 12c2 + 6c3 + 6c2 – 6c2 + 18c + 6c2 + 6c
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 c3 – c2 – c 6c + 6 6c4 + 0c3 – 12c2 + 18c + 19 – 6c4 – 6c3 – 6c3 – 12c2 + 6c3 + 6c2 – 6c2 + 18c + 6c2 + 6c + 24c
Pull the next terms from the original dividend down into the current dividend.
 c3 – c2 – c 6c + 6 6c4 + 0c3 – 12c2 + 18c + 19 – 6c4 – 6c3 – 6c3 – 12c2 + 6c3 + 6c2 – 6c2 + 18c + 6c2 + 6c + 24c + 19
Divide the highest order term in the dividend 24c by the highest order term in divisor 6c.
 c3 – c2 – c + 4 6c + 6 6c4 + 0c3 – 12c2 + 18c + 19 – 6c4 – 6c3 – 6c3 – 12c2 + 6c3 + 6c2 – 6c2 + 18c + 6c2 + 6c + 24c + 19
Multiply the new quotient term by the divisor.
 c3 – c2 – c + 4 6c + 6 6c4 + 0c3 – 12c2 + 18c + 19 – 6c4 – 6c3 – 6c3 – 12c2 + 6c3 + 6c2 – 6c2 + 18c + 6c2 + 6c + 24c + 19 + 24c + 24
The expression needs to be subtracted from the dividend, so change all the signs in 24c+24
 c3 – c2 – c + 4 6c + 6 6c4 + 0c3 – 12c2 + 18c + 19 – 6c4 – 6c3 – 6c3 – 12c2 + 6c3 + 6c2 – 6c2 + 18c + 6c2 + 6c + 24c + 19 – 24c – 24
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 c3 – c2 – c + 4 6c + 6 6c4 + 0c3 – 12c2 + 18c + 19 – 6c4 – 6c3 – 6c3 – 12c2 + 6c3 + 6c2 – 6c2 + 18c + 6c2 + 6c + 24c + 19 – 24c – 24 – 5
The final answer is the quotient plus the remainder over the divisor.
c3-c2-c+4-56c+6
Divide (6c^4-12c^2+18c+19)/(6c+6)

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