Precalculus and Advanced Topics Module 3, Topic A, Overview

Students Commencement Ceremony

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.

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Common Core Learning Standards

CCLS State Standard
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...

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