To find an $x$-intercept, set the profit equal to $0$:

Factor the polynomial:

So the solutions are $x=7$ and $x=-3$. The positive $x$-intercept is $7$.

A product is $0$ only when at least one factor is $0$. So either $x-4=0$ or $x+3=0$. That gives $x=4$ or $x=-3$. Among the choices, the possible value is $4$.

If a graph crosses the $x$-axis at $x=2$ and $x=5$, then the polynomial has zeros at $2$ and $5$. A polynomial with those zeros must include the factors $(x-2)$ and $(x-5)$. So an equivalent expression is $(x-2)(x-5)$.

An $x$-intercept is a point where the graph has $y=0$. Since the graph crosses the $x$-axis at $(3,0)$, the output of the polynomial at $x=3$ is $0$. Therefore, $p(3)=0$.

Because the parabola crosses the $x$-axis at $x=1$ and $x=5$, the polynomial can be written as

Since the graph passes through $(3,-8)$, substitute $x=3$ and $p(3)=-8$:

So $a=2$. Then

Therefore, the value of $p(0)$ is $10$.