Topic A brings students back to the study of complex roots of polynomial functions. Students 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. The topic concludes with students’ use of Cavalieri’s principle to derive formulas for the volume of the sphere and other geometric solids.
Precalculus and Advanced Topics Module 3, Topic A, Overview
Resources may contain links to sites external to the EngageNY.org website. These sites may not be within the jurisdiction of NYSED and in such cases NYSED is not responsible for its content.
Common Core Learning Standards
|N.CN.8||(+) Extend polynomial identities to the complex numbers. For example, rewrite x2 + 4 as (x + 2i)(x...|
|N.CN.9||(+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.|
|A.APR.5||(+) Know and apply the Binomial Theorem for the expansion of (x + y)n in powers of x and y for a...|