# Finite Math Examples

Step 1
To calculate the remainder, first divide the polynomials.
Step 1.1
Reorder and .
Step 1.2
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of .
 + + +
Step 1.3
Divide the highest order term in the dividend by the highest order term in divisor .
 + + +
Step 1.4
Multiply the new quotient term by the divisor.
 + + + + +
Step 1.5
The expression needs to be subtracted from the dividend, so change all the signs in
 + + + - -
Step 1.6
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 + + + - - -
Step 1.7
Pull the next terms from the original dividend down into the current dividend.
 + + + - - - +
Step 1.8
Divide the highest order term in the dividend by the highest order term in divisor .
 - + + + - - - +
Step 1.9
Multiply the new quotient term by the divisor.
 - + + + - - - + - -
Step 1.10
The expression needs to be subtracted from the dividend, so change all the signs in
 - + + + - - - + + +
Step 1.11
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 - + + + - - - + + + +
Step 1.12
The final answer is the quotient plus the remainder over the divisor.
Step 2
Since the last term in the resulting expression is a fraction, the numerator of the fraction is the remainder.