Synthetic Division

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What is Synthetic Division?

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Synthetic Division is a simplified method of dividing a polynomial by a linear binomial of the form (x - c). It is used to find the quotient and remainder without performing long division.

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What is the first step in Synthetic Division?

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The first step is to set up the synthetic division by writing down the coefficients of the polynomial and the zero of the divisor (c) on the left.

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How do you find the zeros of a polynomial using Synthetic Division?

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To find the zeros, perform synthetic division with potential zeros (values of c) and check if the remainder is zero. If the remainder is zero, c is a zero of the polynomial.

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What is the relationship between the degree of the polynomial and the number of zeros?

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A polynomial of degree n can have at most n real zeros, including multiplicities.

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How do you determine if a number is a potential zero of a polynomial?

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A number c is a potential zero if substituting it into the polynomial results in a value of zero.

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What does it mean if the remainder is zero in Synthetic Division?

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If the remainder is zero, it means that the divisor (x - c) is a factor of the polynomial.

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What is the significance of the coefficients in Synthetic Division?

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The coefficients represent the terms of the polynomial, and they are used to perform the division process.