# Find the Remainder 2x^3+x^2-16x-15 ; x-3 ;
Divide the higher order polynomial by the other polynomial in order to find the remainder.
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.
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The expression needs to be subtracted from the dividend, so change all the signs in
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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.
The remainder is the part of the answer that is left after the division by is complete.
Find the Remainder 2x^3+x^2-16x-15 ; x-3     