Remainder Theorem & Factor Theorem

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What is the Remainder Theorem?

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The Remainder Theorem states that if a polynomial P(x) is divided by (x - c), the remainder of this division is P(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 P(x) if and only if P(c) = 0.

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How do you find the remainder of a polynomial when divided by a linear factor?

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To find the remainder of a polynomial P(x) when divided by (x - c), evaluate P(c).

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The remainder is -12.

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The remainder is 19.

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The remainder is -113.

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What is the significance of the remainder in polynomial division?

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The remainder indicates the value of the polynomial at the root of the divisor.

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How can you verify if a polynomial has a factor?

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If P(c) = 0 for a polynomial P(x), then (x - c) is a factor of P(x).