polynomial

Feb 3rd, 2012
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The document discusses the question: If f(x) is a polynomial, then the remainder when f(x) is divided by x-a is f(a). 1) Give a specific example that illustrates the statement. 2) Prove statement.

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1. Lets take f(x) = x^2-2x-1 divided by x-1 as example , Since f(x) = x^2-2x+1-1-1 = (x-1)^2-2, theremainder of f(x) divided by x-1 is -2, and f(1) = 1-2-1 =-2, therefore f(1) =-2.2. Lets assume that the polynomial divided by (x-a) has a quotient of h(x) and remainder b, b mustbe a constant

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