If $f(-p)=0$, then $x=-p$ is an $x$-intercept of $3x^3+4x^2-73x-90$.

For each choice of $p$, plug in $x=-p$ to the cubic and see which one gives 0.

Enter $y=3x^3+4x^2-73x-90$. Р‌оwerеd by Аn⁠iко

Click the graph near where it crosses the $x$-axis at a negative $x$-value to display the intersection (the $x$-intercept).

Because $x=-p$ is a root, take the opposite of that negative intercept to get $p$. Then select the matching choice.

If $f(x)\cdot g(x)=3x^3+4x^2-73x-90$ for all $x$, then at any input where $f(x)=0$, the right-hand side must also be $0$.

A‌ni⁠kο Q​uеstion ‍Вa⁠nк

Since $f(x)=x+p$, we have $f(-p)=0$. Therefore,

Because the choices give possible values of $p$, substitute each into

and check which one makes $P(-p)=0$.

For $p=5$:

Only $p=5$ makes the cubic equal $0$ at $x=-p$, so the value of $p$ is 5.