Polynomial Functions: Zeros, Behavior, and the Structure of Degree n: Math Unit 2, Grade 11 (Letters & Devotion)

Description

Polynomial Functions: Zeros, Behavior, and the Structure of Degree n is Unit 2 of Algebra II: Functions, Structure, and Modeling (Grade 11), the Letters & Devotion Math course, complete in one printable PDF: 11 lessons, the unit check-up and the answer key, 73 pages.

• Multiplicity of a zero as the exponent on its linear factor
• Polynomial long division algorithm
• The logical equivalence between a zero of p and (x-a) being a factor (Remainder/Factor Theorem)
• The Rational Root Theorem as a search-space-narrowing tool
• Factoring by grouping for higher-degree polynomials
• The graphical signature of even vs. odd multiplicity
• End behavior as a function of degree parity and leading coefficient sign
• A polynomial’s graph as the joint product of zeros-with-multiplicity and end behavior
• Reverse-construction of a polynomial equation from graphical/verbal constraints
• Expansion as a check on a factored-form construction
• Factored form vs. standard form as different windows onto the same polynomial

Every lesson is written for a parent with no teaching background: it opens with a short script to read aloud, names the specific wrong idea a student is likely to reach for and how to correct it, and closes with a practice sheet you may copy for your household. Scripture references are King James Version throughout. Black-and-white, 8.5 x 11 in. The whole year of this course is also in this store as a single book.

AI note: The written content of this resource was drafted with AI tools, then reviewed and edited by the author.