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**Standard(s): **
[MA2015] AL2 (9-12) 13 :

[MA2015] AL2 (9-12) 16 :

[MA2015] AL2 (9-12) 17 :

[MA2015] AL2 (9-12) 19 :

[MA2019] AL1-19 (9-12) 30 :

13 ) Use the structure of an expression to identify ways to rewrite it. [A-SSE2]

Example: See *x*^{4} - *y*^{4} as (*x*^{2})^{2} - (*y*^{2})^{2}, thus recognizing it as a difference of squares that can be factored as (*x*^{2} - *y*^{2})(*x*^{2} + *y*^{2}).

[MA2015] AL2 (9-12) 16 :

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]

[MA2015] AL2 (9-12) 17 :

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]

[MA2015] AL2 (9-12) 19 :

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]

[MA2019] AL1-19 (9-12) 30 :

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.

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.