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.

Tags

CCSS.HSA.APR.D.6

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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.

Tags

CCSS.HSA.APR.D.6

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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).

Tags

CCSS.HSA.APR.B.2

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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.

Tags

CCSS.HSA.APR.B.2

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Back

Tags

CCSS.HSA.APR.D.6

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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.

Tags

CCSS.HSA.APR.D.6

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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.

Tags

CCSS.HSA.APR.D.6

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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.

Tags

CCSS.HSA.APR.D.6

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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.

Tags

CCSS.HSA.APR.D.6