# Divide Using Long Polynomial Division (x^4+5x^3-2x^2+5x-3)/(x^2+1)

Divide Using Long Polynomial Division (x^4+5x^3-2x^2+5x-3)/(x^2+1)
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 terms 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 .
 + + + + - + - - - - + - +
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.
 + - + + + - + - - - - + - + - - - - + - + - +
Since the remander is , the final answer is the quotient.
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