The polynomial $2x^3+a{x}^2+bx+6$ is denoted by $p\left(x\right)$.  Given that $(x-3)$ and $(x+2)$ are factors of $p\left(x\right)$, find the value of $a$ and value of $b$.

The polynomials $P\left(x\right)$ and $Q\left(x\right)$ are defined as:

$P\left(x\right)=x^3+a{x}^2+b$ and $Q\left(x\right)=x^3+b{x}^2+a$

It is given that $x-2$ is a factor of $P\left(x\right)$, and that when $Q\left(x\right)$ is divided by $x+1$ the remainder is $-15$ . Find the value of $a$ and the value of $b$.

The polynomials $P\left(x\right)$ and $Q\left(x\right)$ are defined as:

$P\left(x\right)=x^3+a{x}^2+b$ and $Q\left(x\right)=x^3+b{x}^2+a$

It is given that $x-2$ is a factor of $P\left(x\right)$, and that when $Q\left(x\right)$ is divided by $x+1$ the remainder is $-15$. Find the least possible value of $-\left(P\left(x\right)-Q\left(x\right)\right)$ as $x$ varies.