You have the polynomial:

$P(x) = 8x^2 - 4x^3 - 16x^4 + 12x^5$

If you need to perform any operations on this polynomial, like factoring, differentiating, or finding roots, let me know!

Would you like me to do anything specific with this polynomial (such as differentiate, integrate, or simplify)?

Here are 5 related questions to explore:

1. What are the roots of the polynomial $P(x)$?
2. What is the derivative of $P(x)$ with respect to $x$?
3. What is the degree of the polynomial $P(x)$?
4. Can $P(x)$ be factored further?
5. What is the integral of $P(x)$ with respect to $x$?

Tip: When differentiating a polynomial, each term follows the rule $\frac{d}{dx}(ax^n) = nax^{n-1}$.