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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- Sep 12th 2009, 08:01 AMkasia.ogorremainder
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 $\displaystyle a$.

- Sep 12th 2009, 10:11 AMred_dog
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.