# Algebra Examples

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 .
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Divide the highest order term in the dividend by the highest order term in divisor .
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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.
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Pull the next term from the original dividend down into the current dividend.
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Divide the highest order term in the dividend by the highest order term in divisor .
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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.
 + - + - - + + - + - + + - + + - + +
The final answer is the quotient plus the remainder over the divisor.
Since the last term in the resulting expression is a fraction, the numerator of the fraction is the remainder.

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