In this module, students draw on their foundation of the analogies between polynomial arithmetic and base-ten computation, focusing on properties of operations, particularly the distributive property. Students connect multiplication of polynomials with multiplication of multi-digit integers and division of polynomials with long division of integers. Students identify zeros of polynomials, including complex zeros of quadratic polynomials, and make connections between zeros of polynomials and solutions of polynomial equations. Students explore the role of factoring, as both an aid to the algebra and to the graphing of polynomials. Students continue to build upon the reasoning process of solving equations as they solve polynomial, rational, and radical equations, as well as linear and non-linear systems of equations. The module culminates with the fundamental theorem of algebra as the ultimate result in factoring. Students pursue connections to applications in prime numbers in encryption theory, Pythagorean triples, and modeling problems.
To access this resource, you will need to create a free account for the system on which it resides. The partner provides personalized features on their site such as bookmarking and highlighting which requires a user account.

Students encountered the fundamental theorem of algebra, that every polynomial function has at least one zero in the realm of the complex numbers, in Algebra II Module 1. Topic A of this module brings students back to the study of complex roots of polynomial functions. Students first briefly review quadratic and cubic functions and then extend familiar polynomial identities to both complex numbers and to general polynomial functions. Students use polynomial identities to find square roots of complex numbers. The binomial theorem and its relationship to Pascal's triangle are explored using roots of unity. Topic A concludes with student's use of Cavalieri's principle to derive formulas for the volume of the sphere and other geometric solids.
To access this resource, you will need to create a free account for the system on which it resides. The partner provides personalized features on their site such as bookmarking and highlighting which requires a user account.