Final answer:
To find p(0), we consider that the limit of p(x)/q(x) equals 10 and q(0) equals 4. Since the ratio of p(x) to q(x) approaches 10, p(0) must be 10 times q(0), which means p(0) is 40.
Step-by-step explanation:
You are asking about the limit of the ratio of two polynomial functions as x approaches some value. Specifically, you've stated that the limit of the ratio p(x)/q(x) as x approaches some value is 10, and you've also mentioned that q(0) is 4. Based on this information, you want to find p(0).
Since the limit of p(x)/q(x) is 10, it means that as x approaches the value at which the limit is taken (likely 0 in this context), the ratio p(x)/q(x) approaches 10. This implies that p(x) approaches 10 times whatever q(x) approaches. If q(0) is 4, and we're looking at the value of x at 0, then p(0) must be 10 times 4, which means p(0) is 40.