If \( p \) is a polynomial, then \( p \) is continuous at every point. True False

True! Polynomials are made up of continuous operations like addition, subtraction, and multiplication of real numbers. Because of this, they are continuous everywhere on the real number line. So, no matter which point you pick on the polynomial, you can be assured that the function will give you a nice smooth curve with no jumps or breaks. Why does this matter? Well, it means that many powerful mathematical concepts rely on polynomial continuity. For instance, when solving polynomial equations, you can confidently apply the Intermediate Value Theorem to find roots, knowing that the function behaves nicely in between points. Plus, continuity allows us to analyze limits and derivatives seamlessly—important tools in calculus!