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The quadratic expression that leaves remainders 1, 2 and 4 respectively when divided by (x - 1), (x - 2) and (x - 3) is
$$\frac{1}{2}(x^2 + x + 1)$$
$$\frac{1}{2}(x^2 - x + 1)$$
$$\frac{1}{2}(x^2 + x + 2)$$
$$\frac{1}{2}(x^2 - x + 2)$$
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