division, factor and remainder theorem review

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What is the Factor Theorem?

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

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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 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 with the new polynomial until the degree of the remainder is less than the degree of the divisor.

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What is a zero of a polynomial function?

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A zero of a polynomial function f(x) is a value x = c such that f(c) = 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.

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What is synthetic division?

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

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The remainder is 96.

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The zeros are x = 0, 2, 5.

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How do you determine if a polynomial has a specific zero?

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Substitute the value into the polynomial. If the result is zero, then it is a zero of the polynomial.