Precalculus Examples

To calculate the remainder, first divide the polynomials.
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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.
-+
--++
-+
-+
+-
++
-+
+
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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