Final answer:
The question focuses on a polynomial function, specifically how to analyze and understand its roots and graph. The topics mentioned, like completing the square, are fundamental to algebra and covered in high school mathematics.
Step-by-step explanation:
The student's question asks about a given polynomial function f(x)=(x+3)(x+1)² (x-1) and appears to be centered around the topic of understanding polynomial functions, their roots, and possibly graphing them. Polynomials are algebraic expressions that consist of variables and coefficients, involving terms in the form of ax^n where n is a non-negative integer. The provided polynomial can be analyzed to find its roots, the x-values that make the function equal to zero, which are critical in sketching the function's graph and understanding its behavior.
The additional references given in the question, such as completing the square, the solution of quadratic equations, and even and odd functions, are topics that deepen one's understanding of the characteristics of polynomial functions and their solutions. For instance, completing the square is a technique used for solving quadratic functions, which are second-order polynomials, and the concept of even and odd functions helps in analyzing the symmetry of the graph of a given function.
The student's question falls within the scope of algebraic concepts involving polynomial functions, root finding, and graph analysis, which are generally taught in high school mathematics courses. Understanding these concepts is essential for mastering higher-level mathematics and preparing for various standardized tests, such as the SAT.