Synthetic Division

Front

What is synthetic division?

Back

Synthetic division is a simplified method of dividing a polynomial by a linear divisor of the form (x - c), which allows for quicker calculations than long division.

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What is the first step in synthetic division?

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The first step is to write down the coefficients of the polynomial in descending order of degree, using zero as a placeholder for any missing degrees.

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How do you determine the value of 'c' in synthetic division?

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The value of 'c' is determined from the linear divisor (x - c). For example, if the divisor is (x + 3), then c = -3.

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What is the significance of using a zero placeholder in synthetic division?

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Using a zero placeholder ensures that the degrees of the polynomial are correctly represented, which is crucial for accurate calculations.

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What is the result of synthetic division called?

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The result of synthetic division is called the quotient, and it may also include a remainder.

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How do you find the quotient in synthetic division?

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To find the quotient, you perform a series of multiplications and additions using the coefficients of the polynomial and the value of 'c'.

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What is the role of the last number in synthetic division?

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The last number obtained in synthetic division represents the remainder of the division.

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What is the relationship between synthetic division and polynomial long division?

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Synthetic division is a shortcut method for polynomial long division, specifically for dividing by linear factors.

Front

What should you do if a polynomial has missing degrees when using synthetic division?

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You should include zero placeholders for any missing degrees to maintain the correct order of coefficients.

Front

What is the formula for synthetic division when dividing by (x - c)?

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The formula involves writing the coefficients of the polynomial, bringing down the leading coefficient, and then performing a series of multiplications and additions.