# Divide Using Long Polynomial Division (4x^3-3x^2+x+1)÷(x+2)

Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of .
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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 (4x^3-3x^2+x+1)÷(x+2)