The function f(x) = ax 3 + 4x 2 + bx 2, where a and b

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The function f(x) = ax3 + 4x2 + bx – 2, where a and b are constants, is such that 2x – 1 is a factor. Given that the remainder when f(x) is divided by x – 2 is twice the remainder when f(x) is divided by x + 1, find the value of a and of b.

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