Find the Remainder (x^5+5x^3-9x+1)/(x^2+6)


Step 1
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.
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-+-
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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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-+-
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Pull the next term from the original dividend down into the current dividend.
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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.


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