Polynomial Long and Synthetic Division

Front

What is Polynomial Long Division?

Back

A method for dividing a polynomial by another polynomial of the same or lower degree, similar to long division with numbers.

Front

What is Synthetic Division?

Back

A simplified form of polynomial division that is used when dividing by a linear factor, typically represented as (x - c).

Front

How do you set up Synthetic Division?

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Write the coefficients of the polynomial in a row, and place the zero of the divisor (c) to the left.

Front

What is the purpose of adding zeros in Synthetic Division?

Back

To ensure that all degrees of the polynomial are represented, making the division process easier.

Front

What does the left-hand box represent in Synthetic Division?

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It represents the zero of the divisor, which is used to perform the division.

Front

What is the first step in Polynomial Long Division?

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Divide the leading term of the dividend by the leading term of the divisor.

Front

What do you do after finding the first term in Long Division?

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Multiply the entire divisor by the term found and subtract the result from the dividend.

Front

What is the remainder in Polynomial Division?

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The value left over after dividing a polynomial, which can be expressed as a fraction of the divisor.

Front

How do you check your work in Polynomial Long Division?

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Multiply the quotient by the divisor and add the remainder; the result should equal the original dividend.

Front

What is the significance of changing signs in Synthetic Division?

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It ensures that the correct values are subtracted during the division process.