# Find the Remainder (3x^4+2x^3-x^2+2x-24)/(x+2)

To calculate the remainder, first divide the polynomials.
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.
 – + + + – + – – – – – + + + + – – –
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.
 – + – + + – + – – – – – + + + + – – – – + +
Since the remander is , the final answer is the quotient.
Since the final term in the resulting expression is not a fraction, the remainder is .
Find the Remainder (3x^4+2x^3-x^2+2x-24)/(x+2)