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Remainder of Polynomial Division

Source:

January 11, 2009
algebrapolynomialsystem of equations

Problem Statement

Let P(x) P(x) be a polynomial such that when P(x) P(x) is divided by x \minus{} 19, the remainder is 99 99, and when P(x) P(x) is divided by x \minus{} 99, the remainder is 19 19. What is the remainder when P(x) P(x) is divided by (x \minus{} 19)(x \minus{} 99)? (A)\ \minus{}x \plus{} 80 \qquad (B)\ x \plus{} 80 \qquad (C)\ \minus{}x \plus{} 118 \qquad (D)\ x \plus{} 118 \qquad (E)\ 0
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