Polynomial Long Division

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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 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 determine if a binomial is a factor of a polynomial?

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A binomial is a factor of a polynomial if the polynomial evaluates to zero when the binomial is set to zero.

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What does it mean if the remainder is zero in Polynomial Long 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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Perform the division: 2x^3 + 5x^2 + 9 ÷ (x + 3). What is the result?

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2x^2 - x + 3.

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Perform the division: 2x^3 - 5x^2 + 3x + 7 ÷ (x - 2). What is the result?

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2x^2 - x + 1 + 9/(x - 2).

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What is the significance of the leading coefficient in Polynomial Long Division?

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The leading coefficient helps determine the degree of the quotient and the behavior of the polynomial as x approaches infinity.

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What is synthetic division and how does it relate to Polynomial Long Division?

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Synthetic division is a simplified form of polynomial long division that is used when dividing by a linear factor.

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What is the Remainder Theorem?

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The Remainder Theorem states that the remainder of the division of a polynomial f(x) by (x - c) is equal to f(c).

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What is the Factor Theorem?

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The Factor Theorem states that (x - c) is a factor of f(x) if and only if f(c) = 0.