If $x+4$ is a factor of the polynomial $x^{2}+7x+m$,then $m = $ . . . . . .

The product of the zeros of the polynomial $kx^{3}-6x^{2}+11x-6$ is $4$. Find the value of $k$.

If $1$ and $3$ are the zeros of the polynomial $p(x) = 2x^4 - 7x^3 - 13x^2 + 63x - 45$,then find the remaining zeros of $p(x)$.

Find the division of the following by synthetic division method: $p(x) = x^{3} - 4x^{2} + 5x + 3$ by $x - 2$.

Are the following statements 'True' or 'False'? Justify your answers.
If all three zeroes of a cubic polynomial $x^{3}+ax^{2}-bx+c$ are positive,then at least one of $a, b$ and $c$ is non-negative.

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