If one factor of $x^{3}+4 x^{2}+8 x+a$ is $(x+2)$,then find the value of $a$.

What must be added to the polynomial $p(x) = 6x^5 + 5x^4 + 11x^3 - 3x^2 + x + 1$ so that the resulting polynomial is exactly divisible by $3x^2 - 2x + 4$? (Hint: add $-r(x)$ to $p(x)$)

If the zeros of the cubic polynomial $p(x) = ax^3 + bx^2 + cx + d$ $(a \neq 0, a, b, c, d \in R)$ are $\alpha, \beta,$ and $\gamma$,then $\alpha\beta + \beta\gamma + \gamma\alpha = \dots$

Identify the type of the given polynomial based on its degree: $p(x) = (x - 1)(2 - x)$

Obtain the value of the following polynomial at the given value of $x$: $p(x) = x^{4} + 2x^{3} - x + 2$; at $x = 2$.

The graph of $p(x) = x^{2} - x - 2$ intersects the $X$-axis at: