2.3.22 Dividing Polynomials- 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 divisor of the form (x - c). It is faster and requires less writing 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 the coefficients of the polynomial in descending order and place the value of c (from x - c) in a box on the left.

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How do you handle missing terms in synthetic division?

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If there are missing terms in the polynomial, use a coefficient of 0 for that term when writing the coefficients.

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What does the remainder represent in synthetic division?

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The remainder represents the value of the polynomial at the divisor's root. If the remainder is 0, it means the divisor is a factor of the polynomial.

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How do you find the value of a polynomial at a specific point using synthetic division?

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To find f(c) using synthetic division, divide the polynomial by (x - c) and the remainder will be f(c).

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What is the significance of the number in the left-hand box during synthetic division?

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The number in the left-hand box represents the root of the divisor (c) in the expression (x - c).

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What is the final form of the answer when dividing a polynomial by synthetic division?

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f(-2) = 0.

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What is the relationship between synthetic division and polynomial roots?

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If synthetic division yields a remainder of 0, then the divisor (x - c) is a root of the polynomial.