A polynomial \( P \) is positive for \( x0 \) and the area of the r...

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A polynomial \( P \) is positive for \( x0 \) and the area of the region bounded by \( P(x) \), the \( x \)-axis, and the vertical lines \( x=0 \) and \( x=k \) is \( k^{2}(k+3) / 3 \). The polynomial \( P(x) \) is
(a) \( x^{2}+x+1 \)
(b) \( x^{2}+2 x+1 \)
(c) \( x^{2}+2 x \)
(d) \( x^{3}+1 \)
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