Polynomial Long Division & Remainder Theorem

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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 if a polynomial f(x) is divided by (x - c), the remainder of this division is f(c).

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

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To determine if (x - c) is a factor of f(x), evaluate f(c). If f(c) = 0, then (x - c) is a factor.

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What is a zero of a polynomial function?

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A zero of a polynomial function is a value of x for which the polynomial evaluates to zero, meaning f(x) = 0.

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How do you find the zeros of a polynomial?

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To find the zeros of a polynomial, set the polynomial equal to zero and solve for x using factoring, the quadratic formula, or synthetic division.

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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 factors and zeros of a polynomial?

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If (x - c) is a factor of a polynomial f(x), then c is a zero of f(x).

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What does it mean for a polynomial to be factored completely?

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A polynomial is factored completely when it is expressed as a product of irreducible polynomials over the given number system.

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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 expression.

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What is the leading coefficient of a polynomial?

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