Title: |
Algebra II Module 1, Topic B: Factoring--Its Use and Its Obstacles |
URL: |
https://www.engageny.org/resource/algebra-ii-module-1-topic-b-overview |
Content Source: |
EngageNY
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Type: |
Lesson/Unit Plan
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Overview: |
Module 1, Topic B focuses on factoring polynomials and the advantages of factored form of a polynomial to both solve equations and sketch graphs of polynomial functions. Students solve problems involving real-world situations and develop fluency with creating equations and functions given a verbal description, visual representation, or graph. This topic concludes with a discussion of polynomial division with remainder, further strengthening the connection between the remainder, the factors and zeros of a polynomial equation, and graphs of polynomial functions. |
Content Standard(s): |
Mathematics MA2015 (2016) Grade: 9-12 Algebra II | 13 ) Use the structure of an expression to identify ways to rewrite it. [A-SSE2]
Example: See x4 - y4 as (x2)2 - (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 - y2)(x2 + y2). | Mathematics MA2015 (2016) Grade: 9-12 Algebra II | 16 ) Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x - a is p(a), so p(a) = 0 if and only if (x - a) is a factor of p(x). [A-APR2] | Mathematics MA2015 (2016) Grade: 9-12 Algebra II | 17 ) Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. [A-APR3] | Mathematics MA2015 (2016) Grade: 9-12 Algebra II | 19 ) Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or for the more complicated examples, a computer algebra system. [A-APR6] | Mathematics MA2019 (2019) Grade: 9-12 Algebra I with Probability | 30. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
a. Graph linear and quadratic functions and show intercepts, maxima, and minima.
b. Graph piecewise-defined functions, including step functions and absolute value functions.
c. Graph exponential functions, showing intercepts and end behavior. Unpacked Content
Alabama Alternate Achievement Standards
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Tags:
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division, equation, expressions, factor, functions, graph, polynomial, rational, Remainder Theorem |
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Accessibility | Text Resources: Content is organized under headings and subheadings |
Comments | There are ten lessons on this topic.
This resource is free for teachers to access and use. All resources required for the lessons are available to print from the site. |