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**jgv115** The polynomial $\displaystyle P(x)$ has a remainder of 2 when divided by $\displaystyle x-1$ and a remainder of 3, when divided by $\displaystyle x-2$. The remainder when $\displaystyle P(x)$ is divided by$\displaystyle (x-1)(x-2)$ is $\displaystyle ax + b$, i.e. $\displaystyle P(x)$ can be written as $\displaystyle P(x) = (x-1)(x-2)Q(x)+ax+b$

Find a and b.

Well I got this already a= 1 and b=1

but the second question I don't know what to do...

Given that$\displaystyle P(x)$ is a cubic polynomial with coefficient of $\displaystyle x^3$ being 1, and −1 is a solution of the equation $\displaystyle P(x) = 0$, find $\displaystyle P(x)$.

I'm not too sure how to start... If -1 is a solution of the question when $\displaystyle P(x) = 0$ that means $\displaystyle (x+1)$ must be a factor right? I don't know what to do from here...

All replies are appreciated