Determine whether $(x+1)$ is a factor of the polynomial $p(x) = x^{3} - 2x^{2} - 5x + 6$.

What are the possible expressions for the dimensions of the cuboids whose volumes are given below? $\boxed{\text{Volume} : 3x^2 - 12x}$

For the polynomial $p(x),$ if $p(7)=0,$ then .......... is a factor of $p(x)$.

Check whether $p(x)$ is a multiple of $g(x)$ or not,where $p(x) = x^{3} - x + 1$ and $g(x) = 2 - 3x$.

With the help of the remainder theorem,find the remainder when the polynomial $p(x) = x^{3} + x^{2} - 26x + 24$ is divided by the divisor $x - 4$.

If both $x-2$ and $x-\frac{1}{2}$ are factors of $p x^{2}+5 x+r,$ show that $p=r$.