Synthetic Division

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What is Synthetic Division?

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A method used to divide a polynomial by a binomial of the form (x - c) without using long division.

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What is a dividend in polynomial division?

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The polynomial that is being divided. For example, in the division of f(x) by (x - c), f(x) is the dividend.

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What is a divisor in polynomial division?

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The polynomial by which the dividend is divided. In the expression f(x) ÷ (x - c), (x - c) is the divisor.

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What is a remainder in polynomial division?

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The value left over after division when the dividend is not evenly divisible by the divisor.

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How do you determine if (x - c) is a factor of a polynomial?

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If the remainder is zero when dividing the polynomial by (x - c), then (x - c) is a factor.

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What is the relationship between the degree of the dividend and the divisor?

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The degree of the dividend must be greater than or equal to the degree of the divisor for synthetic division to be applicable.

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What is the first step in synthetic division?

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Write down the coefficients of the dividend polynomial.

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How do you set up synthetic division?

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Place the value of c (from (x - c)) to the left and the coefficients of the dividend in a row.

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What is the purpose of bringing down the first coefficient in synthetic division?

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It starts the process of combining coefficients to find the quotient.

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What do you do after bringing down the first coefficient in synthetic division?

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Multiply the value of c by the coefficient just brought down and add it to the next coefficient.