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 .

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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 .

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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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Since the remander is , the final answer is the quotient.

Divide Using Long Polynomial Division (3x^4+7x^3+2x^2+13x+5)÷(x^2+3x+1)