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 of the form (x - c).

Front

What is the first step in Synthetic Division?

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Write down the coefficients of the polynomial being divided.

Front

How do you determine the number of zeros needed in Synthetic Division?

Back

Count the degree of the polynomial being divided and use that number of zeros in the top row.

Front

What does a zero placeholder represent in Synthetic Division?

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It represents a missing term in the polynomial, ensuring the correct alignment of coefficients.

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What is the role of the divisor in Synthetic Division?

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The divisor is the linear factor (x - c) that you are dividing by, where 'c' is the value used in the synthetic division process.

Front

What is the significance of the remainder in Polynomial Division?

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The remainder indicates what is left over after division; if it is zero, the divisor is a factor of the polynomial.

Front

What mistake did Cam make in his Synthetic Division?

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He did not use a zero placeholder for the x^3 term.

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How do you check the correctness of a Polynomial Division?

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

Front

What happens if you add instead of subtract in Synthetic Division?

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It leads to incorrect coefficients in the quotient, resulting in an incorrect answer.