Dividing Polynomials

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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 numerical long division.

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What is the remainder theorem?

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

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How do you determine if (x - c) is a factor of a polynomial?

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To determine if (x - c) is a factor of a polynomial, use the factor theorem: if f(c) = 0, then (x - c) is a factor.

Front

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 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 a leading coefficient?

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The leading coefficient is the coefficient of the term with the highest degree in a polynomial.

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What is the quotient in polynomial division?

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The quotient is the result obtained from dividing one polynomial by another.

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What is a polynomial?

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A polynomial is a mathematical expression consisting of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication.

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What does it mean for a polynomial to be divided by a linear factor?

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Dividing a polynomial by a linear factor means finding how many times the linear factor can fit into the polynomial, resulting in a quotient and possibly a remainder.

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What is the significance of the number of zeros in synthetic division?

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The number of zeros needed in synthetic division corresponds to the degree of the polynomial minus the number of terms being divided.