Final answer:
A polynomial of degree 12 has a maximum of 12 x intercepts, but the actual number can be less if some roots are complex or repeated.
Step-by-step explanation:
The maximum number of x intercepts that a polynomial of degree 12 can have is 12. This is because the Fundamental Theorem of Algebra states that a polynomial of degree n will have exactly n roots, however, not all roots are necessarily real and distinct. In a real-world context, if the polynomial represents a function such as f(x), it can intersect the x-axis at most 12 times when we are considering real numbers only.
The x intercept(s) of a graph occur(s) when the output f(x) is zero. Therefore, a polynomial of degree 12 can have up to 12 x intercepts, considering the roots are distinct. However, if some of the roots are complex or repeated, the actual number of x intercepts could be less.