CRM 3.2 - Synthetic and Long Division Review

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What is synthetic division?

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Synthetic division is a simplified form of polynomial long division that is used when dividing a polynomial by a linear factor 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 set up the synthetic division by writing the coefficients of the polynomial in descending order of degree and placing the value of c (from x - c) to the left.

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How do you determine the coefficients of a polynomial?

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The coefficients of a polynomial are the numerical factors in front of each term, arranged in descending order of the variable's exponent.

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What is the remainder theorem?

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The remainder theorem states that if a polynomial f(x) is divided by (x - c), the remainder of that division is f(c).

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What does it mean for (x + 3) to be a factor of a polynomial?

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If (x + 3) is a factor of a polynomial, it means that when the polynomial is divided by (x + 3), the remainder is zero.

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

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Using a zero placeholder is important to maintain the correct alignment of terms, especially when a term is missing in the polynomial.

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How do you find the quotient in polynomial long division?

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To find the quotient, divide the leading term of the dividend by the leading term of the divisor, then multiply the entire divisor by this result and subtract from the dividend.

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What is the purpose of polynomial long division?

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Polynomial long division is used to divide polynomials to find the quotient and remainder, similar to numerical long division.

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What is the relationship between synthetic division and long division?

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