If the zero of the polynomial $p(x) = 3x^{3} - x^{2} - ax - 45$ is $3$,then $a = \dots$

Identify the type of the following polynomial based on its degree: $p(x) = 7 - 5x$.

Examine the validity of the following statement: $(x-2)$ is a factor of $x^{3}+5x^{2}-2x-25$.

The zeroes of the quadratic polynomial $x^{2}+kx+k, k \neq 0,$

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 $\alpha + \beta + \gamma = \ldots$

Find the division of the following by synthetic division method: $p(t) = 2t^2 + 3t + 1$ by $t + 2$.