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Let T:P3→P3 be the linear transformation such that T(−2x2)=−3x2+3x, T(0.5x−4)=4x2−2x−2, and T(2x2−1)=3x−3.
Find T(1), T(x), T(x2), and T(ax2+bx+c), where a, b, and c are arbitrary real numbers.

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