Polynomial Long Division & Synthetic Division Practice

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What is Polynomial Long Division?

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Polynomial Long Division is 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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Synthetic Division is a simplified form of polynomial long division that is used when dividing by a linear factor of the form (x - c). It is faster and requires less writing.

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What is the first step in Polynomial Long Division?

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The first step is to divide the leading term of the dividend by the leading term of the divisor.

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How do you handle missing exponents in a polynomial?

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You must place a zero as a coefficient for any missing exponent to maintain the correct degree of the polynomial.

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What does it mean if the remainder is zero in polynomial division?

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If the remainder is zero, it means that the divisor is a factor of the dividend.

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What is the relationship between the degree of the dividend and the divisor in polynomial division?

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The degree of the dividend must be greater than or equal to the degree of the divisor for polynomial division to be valid.

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What is the purpose of the quotient in polynomial division?

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The quotient represents how many times the divisor fits into the dividend, and it is the result of the division.

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What is the standard form of a polynomial?

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The standard form of a polynomial is written in descending order of the degree of its terms, from highest to lowest.

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How do you check your work after performing polynomial long division?

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You can check your work by multiplying the quotient by the divisor and adding the remainder; the result should equal the original dividend.