Final answer:
The mass of the star is the important factor to predict whether it will fuse oxygen into heavier elements in its core.
Step-by-step explanation:
The fact about the star that you need to know in order to predict whether it will eventually fuse oxygen into heavier elements in its core is the star's mass.
The higher the mass of the star, the higher the pressure and temperature in its core, which can allow fusion reactions to occur. Massive stars, with a mass greater than about 8 solar masses, can fuse oxygen into heavier elements such as neon, magnesium, and silicon.
Therefore, the star's mass is a crucial factor in determining its ability to fuse oxygen and other elements in its core.