Divide (12m^2+57+66)÷(4m+11)

(12m2+57+66)÷(4m+11)
12m2+1234m+11
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of 0.
 4m + 11 12m2 + 0m + 123
Divide the highest order term in the dividend 12m2 by the highest order term in divisor 4m.
 3m 4m + 11 12m2 + 0m + 123
Multiply the new quotient term by the divisor.
 3m 4m + 11 12m2 + 0m + 123 + 12m2 + 33m
The expression needs to be subtracted from the dividend, so change all the signs in 12m2+33m
 3m 4m + 11 12m2 + 0m + 123 – 12m2 – 33m
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 3m 4m + 11 12m2 + 0m + 123 – 12m2 – 33m – 33m
Pull the next terms from the original dividend down into the current dividend.
 3m 4m + 11 12m2 + 0m + 123 – 12m2 – 33m – 33m + 123
Divide the highest order term in the dividend -33m by the highest order term in divisor 4m.
 3m – 334 4m + 11 12m2 + 0m + 123 – 12m2 – 33m – 33m + 123
Multiply the new quotient term by the divisor.
 3m – 334 4m + 11 12m2 + 0m + 123 – 12m2 – 33m – 33m + 123 – 33m – 3634
The expression needs to be subtracted from the dividend, so change all the signs in -33m-3634
 3m – 334 4m + 11 12m2 + 0m + 123 – 12m2 – 33m – 33m + 123 + 33m + 3634
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 3m – 334 4m + 11 12m2 + 0m + 123 – 12m2 – 33m – 33m + 123 + 33m + 3634 + 8554
The final answer is the quotient plus the remainder over the divisor.
3m-334+8554(4m+11)
Divide (12m^2+57+66)÷(4m+11)