Polynomial Division and Review of Inequalities

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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 Synthetic Division?

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Synthetic Division is a simplified method of dividing a polynomial by a linear divisor of the form (x - c). It is faster and requires less writing than 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 of this division is 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 the polynomial f(x) if and only if f(c) = 0.

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How do you solve inequalities involving polynomials?

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To solve polynomial inequalities, first find the roots of the polynomial, then test intervals between the roots to determine where the inequality holds true.

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What does it mean for a polynomial to be greater than zero?

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A polynomial is greater than zero when its values are positive for the given range of x.

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What does it mean for a polynomial to be less than zero?

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A polynomial is less than zero when its values are negative for the given range of x.

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What is an example of a polynomial?

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