Divide Using Long Polynomial Division (12m^7-8m^5+16m^4+6m^2)÷4m^3

Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of .
 + + + + – + + + + +
Divide the highest order term in the dividend by the highest order term in divisor .
 + + + + – + + + + +
Multiply the new quotient term by the divisor.
 + + + + – + + + + + + + + +
The expression needs to be subtracted from the dividend, so change all the signs in
 + + + + – + + + + + – – – –
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 + + + + – + + + + + – – – – – +
Pull the next term from the original dividend down into the current dividend.
 + + + + – + + + + + – – – – – + + +
Divide the highest order term in the dividend by the highest order term in divisor .
 + – + + + + – + + + + + – – – – – + + +
Multiply the new quotient term by the divisor.
 + – + + + + – + + + + + – – – – – + + + – + + +
The expression needs to be subtracted from the dividend, so change all the signs in
 + – + + + + – + + + + + – – – – – + + + + – – –
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 + – + + + + – + + + + + – – – – – + + + + – – – + + +
Pull the next term from the original dividend down into the current dividend.
 + – + + + + – + + + + + – – – – – + + + + – – – + + + + +
Divide the highest order term in the dividend by the highest order term in divisor .
 + – + + + + + – + + + + + – – – – – + + + + – – – + + + + +
Multiply the new quotient term by the divisor.
 + – + + + + + – + + + + + – – – – – + + + + – – – + + + + + + + + +
The expression needs to be subtracted from the dividend, so change all the signs in
 + – + + + + + – + + + + + – – – – – + + + + – – – + + + + + – – – –
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 + – + + + + + – + + + + + – – – – – + + + + – – – + + + + + – – – – + +
Pull the next terms from the original dividend down into the current dividend.
 + – + + + + + – + + + + + – – – – – + + + + – – – + + + + + – – – – + + +
The final answer is the quotient plus the remainder over the divisor.
Divide Using Long Polynomial Division (12m^7-8m^5+16m^4+6m^2)÷4m^3