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Chapter 3: Problem 61

State the Remainder Theorem.

Short Answer

Expert verified
The Remainder Theorem states that if a polynomial \(P(x)\) is divided by \((x - a)\), then the remainder is equal to the value of the polynomial at \(x = a\), which is represented as \(P(a)\).

Step by step solution

01

Identify the Theorem

The Remainder Theorem states that for a polynomial \( P(x) \) and a number \( a \), when you divide \( P(x) \) by \( x-a \), the remainder is \( P(a) \)
02

Explain the Theorem

This theorem basically defines that if a polynomial \(P(x)\) is divided by \((x - a)\), then the remainder is equal to the value of the polynomial at \(x = a\), which is described as \(P(a)\). It essentially allows us to find the remainder of a polynomial division without performing the actual division operation.

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