The high school curriculum sometimes seems like a disconnected collection of topics and techniques. Theorems like the factor theorem and the remainder theorem can play an important role as a conceptual "glue" that holds the curriculum together. These two theorems establish the connection between the factors of a polynomial, the solutions to a polynomial equation, and the graph of a polynomial function. They generalize what is previously learned in first-year algebra, reinforce important ideas about proof that students learn in geometry, and foreshadow important ideas of calculus. There is much more to appreciate about these two theorems than one might think.