X^2-4x-12+2x^3How to

To solve the expression X^2 - 4x - 12 + 2x^3, we can start by rearranging the terms in standard polynomial form, which means ordering the terms in descending powers of x.

1. We have 2x^3, which is the term with the highest degree (degree 3).
2. Next is X^2 (degree 2).
3. Then we have -4x (degree 1).
4. Finally, we have the constant term -12.

We can rewrite the expression as follows:

2x^3 + X^2 - 4x - 12

This is a polynomial of degree 3. To analyze or solve this polynomial, we can perform different operations depending on what is required:

- If we want to factor or find roots, we can set the expression equal to zero and solve for x:
2x^3 + X^2 - 4x - 12 = 0

- We can use methods like synthetic division, factoring, or the Rational Root Theorem to find potential rational roots.

- Alternatively, we could graph the polynomial to find approximate zeros, or use numerical methods if necessary.

Note that to actually find specific roots or factors, we would need to apply further methods such as finding possible rational roots or using numerical methods, which may not yield simple factoring due to the cubic term and the coefficients involved. The solutions to the cubic equation can be complex and may require methods such as Cardano's formula for exact solutions or numerical approximations.