Given the polynomial \( P(x) = 4x^3 - 5x^2 + 3x - 7 \), use the Remainder Theorem to find the remainder when \( P(x) \) is divided by \( x - 2 \). Then, using polynomial division, find the quotient and remainder of the division of \( P(x) \) by \( x - 2 \). Compare the remainder obtained by the Remainder Theorem and polynomial division. Let's think step by step and output the final answer within \boxed{}.
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