Polynomial Division

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What is polynomial division?

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Polynomial division is the process of dividing a polynomial by another polynomial of the same or lower degree, similar to long division with numbers.

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What is the degree of a polynomial?

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The degree of a polynomial is the highest power of the variable in the polynomial.

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What is the quotient in polynomial division?

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The quotient is the result of dividing one polynomial by another.

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What is the remainder in polynomial division?

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The remainder is what is left over after dividing one polynomial by another, which can be expressed as a fraction of the divisor.

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How do you perform polynomial long division?

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1. Divide the leading term of the dividend by the leading term of the divisor. 2. Multiply the entire divisor by this result. 3. Subtract this from the dividend. 4. Repeat the process with the new polynomial.

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What is synthetic division?

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Synthetic division is a simplified form of polynomial division that is used when dividing by a linear factor of the form (x - c).

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What is the relationship between the degree of the dividend and the divisor?

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The degree of the quotient will be the degree of the dividend minus the degree of the divisor.

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What is the significance of the remainder in polynomial division?

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The remainder indicates whether the divisor is a factor of the dividend. If the remainder is zero, the divisor is a factor.

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How can you check your work after polynomial 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.

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