# Divide Using Long Polynomial Division (25a^4+19a^2-a-78)÷(5a^2+6a-9)

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 terms 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.
 – + – + + – – – – + – + – + + – + – –
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.
 – + + – + + – – – – + – + – + + – + – – – – + – +
The final answer is the quotient plus the remainder over the divisor.
Divide Using Long Polynomial Division (25a^4+19a^2-a-78)÷(5a^2+6a-9)