This task looks at zeroes and factorization of a general polynomial. It is related to a very deep theorem in mathematics, the Fundamental Theorem of Algebra, which says that a polynomial of degree d always has exactly d roots, provided complex numbers are allowed as roots and provided roots are counted with the proper "multiplicity.''

The intention of this task is to provide extra depth to the standard A-APR.2 it is principally designed for instructional purposes only. The students may use graphing technology: the focus, however, should be on what happens to the function g when x=0 and the calculator may or may not be of help here (depending on how sophisticated it is!).

For a polynomial function p, a real number r is a root of p if and only if p(x) is evenly divisible by x_r. This fact leads to one of the important properties of polynomial functions: a polynomial of degree d can have at most d roots. This is the first of a sequence of problems aiming at showing this fact.

This task continues ``Zeroes and factorization of a quadratic polynomial I.'' The argument here generalizes, as shown in ``Zeroes and factorization of a general polynomial'' to show that a polynomial of degree d can have at most d roots. This task is intended for instructional purposes to help students see more clearly the link between factorization of polynomials and zeroes of polynomial functions.

Students experience the engineering design process as they design and construct lower-leg prostheses in response to a hypothetical zombie apocalypse scenario. Like the well-known Apollo 13 story during which engineers were challenged to fix the crippled spacecraft with limited supplies in order to save astronauts' lives, in this activity, students act as engineers during an imaginary disaster in which a group member's leg was amputated in order to survive a zombie attack. Building on what they learned and researched in the associated lesson, they design and fabricate a replacement prosthetic limb using given specific starting material and limited additional supplies, similar to how engineers design for individuals while working within constraints. A more-advanced scenario challenges students to design a prosthesis that is able to provide a more-specific movement function.

Thought provoking questions and links that will help educators discuss digital citizenship witth their students.