iran-konkur 2021 Q108

iran-konkur · Other · konkur-riazi_1400_specialized Polynomial Division & Manipulation
108- $P(x)$ is a second-degree polynomial with natural coefficients. If $P(x)$ is divided by $P'(x)$ (the derivative of $P(x)$), the quotient and remainder are $\dfrac{1}{2}x + 1$ and $2-$, respectively. What is the minimum value of the sum of the coefficients of $P(x)$?
(1) $4$ (2) $6$ (3) $7$ (4) $9$
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\textbf{108-} $P(x)$ is a second-degree polynomial with natural coefficients. If $P(x)$ is divided by $P'(x)$ (the derivative of $P(x)$), the quotient and remainder are $\dfrac{1}{2}x + 1$ and $2-$, respectively. What is the minimum value of the sum of the coefficients of $P(x)$?

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(1) $4$ \hfill (2) $6$ \hfill (3) $7$ \hfill (4) $9$



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