Alg 2 - Polynomial Long & Synthetic Division

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What is Polynomial Long Division?

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A method used to divide a polynomial by another polynomial of the same or lower degree, similar to long division with numbers.

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What is Synthetic Division?

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A shortcut method for dividing a polynomial by a linear divisor of the form (x - c), which simplifies calculations.

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How do you determine the number of placeholder zeros needed in polynomial division?

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The number of placeholder zeros is equal to the difference in degrees between the dividend and the divisor.

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What is the degree of a polynomial?

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The highest power of the variable in the polynomial.

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What is the remainder theorem?

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If a polynomial f(x) is divided by (x - c), the remainder is f(c).

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What is the quotient in polynomial division?

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The result obtained from dividing one polynomial by another.

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What is the significance of the leading coefficient in polynomial division?

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It helps determine the first term of the quotient during polynomial long division.

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How do you perform synthetic division?

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1. Write the coefficients of the polynomial. 2. Use the root of the divisor (c) to perform the division process.

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