the remainder obtained when $\displaystyle 2x^3 + ax^2 - 6x + 1 $ is divided by $\displaystyle (x+2)$ is twice the remainder obtained when the same expression is divided by $\displaystyle (x-1)$. Find the value of $\displaystyle a$.
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Let $\displaystyle P(x)=2x^3+ax^2-6x+1$ The remainder when dividing by $\displaystyle x+2$ is $\displaystyle P(-2)$ The remainder when dividing by $\displaystyle x-1$ is $\displaystyle P(1)$ Then we have $\displaystyle P(-2)=2P(1)$ Now find a.
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