Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

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Divide the highest order term in the dividend <math><mstyle displaystyle="true"><msup><mrow><mi>x</mi></mrow><mrow><mn>4</mn></mrow></msup></mstyle></math> by the highest order term in divisor <math><mstyle displaystyle="true"><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

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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 <math><mstyle displaystyle="true"><msup><mrow><mi>x</mi></mrow><mrow><mn>4</mn></mrow></msup><mo>+</mo><mn>0</mn><mo>+</mo><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math>

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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 <math><mstyle displaystyle="true"><mn>5</mn><msup><mrow><mi>x</mi></mrow><mrow><mn>3</mn></mrow></msup></mstyle></math> by the highest order term in divisor <math><mstyle displaystyle="true"><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

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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 <math><mstyle displaystyle="true"><mn>5</mn><msup><mrow><mi>x</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>+</mo><mn>0</mn><mo>+</mo><mn>5</mn><mi>x</mi></mstyle></math>

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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 <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> by the highest order term in divisor <math><mstyle displaystyle="true"><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

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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 <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mn>0</mn><mo>-</mo><mn>3</mn></mstyle></math>

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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 <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> , the final answer is the quotient.

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