Section	Teacher-facing learning goals
What Is a Polynomial?	Lesson 1 Generalize from specific calculations to create a polynomial to model the volume of a constructed box. Interpret features of a graph of a polynomial. Lesson 2 Create a polynomial to model a simple investment situation. Generalize the structure of integers in order to see similarities to polynomials. Lesson 3 Identify relative minimums and relative maximums of graphs of polynomials. Identify the degree, leading term, and constant term of a polynomial. Lesson 4 Comprehend that when polynomials are combined by addition, subtraction, or multiplication, the result is a polynomial. Justify (orally) conclusions about what happens when integers or polynomials are combined using arithmetic operations.
Working with Polynomials	Lesson 5 Identify zeros of polynomial functions written in factored form. Understand that if factors multiplied together equal zero for a specific value of \(x\), at least one of the factors must also equal zero at that value of \(x\). Lesson 6 Comprehend that all polynomials can be written in standard and factored forms. Describe features of polynomial graphs and expressions using precise language. Identify properties of polynomials by representing them in equivalent forms. Lesson 7 Explain how to find an appropriate graphing window for a function in factored form. Generate a possible expression for a polynomial function given the horizontal intercepts of the function. Lesson 8 Compare and contrast (orally) the end behavior of polynomials of even and odd degree. Generalize about end behavior based on specific functions and calculations. Identify end behavior of polynomial functions from equations. Lesson 9 Comprehend how the sign of the leading coefficient of a polynomial function affects the end behavior. Create equations for polynomial functions with specific end behavior. Lesson 10 Comprehend the effect that the multiplicity of factors has on the shape of the graph of a polynomial function. Use zeros and multiplicities to create a rough graph of a polynomial function given in factored form. Lesson 11 Calculate the solution to a system of polynomial equations. Lesson 12 Calculate the result of polynomial division using a diagram. Identify factors of polynomials using division. Lesson 13 Compare and contrast diagrams and long division as ways of representing division. Use long division to find the quotient of two polynomials. Lesson 14 Determine what information is needed to sketch a polynomial function given a known factor. Ask questions to elicit that information. Lesson 15 Comprehend that for a polynomial \(p(x)\) and a number \(a\), the remainder on division by \((x-a)\) is \(p(a)\). Comprehend that for a polynomial \(p(x)\), \((x-a)\) is a factor if \(p(a)=0\) and, conversely, that \(p(a)=0\) if \((x-a)\) is a factor.
Rational Functions	Lesson 16 Create a rational function to model the surface area of a cylinder of known volume. Interpret graphs of rational functions in context. Lesson 17 Identify features of simple rational functions from graphs and equations. Interpret the end behavior of a rational function in context. Lesson 18 Identify horizontal asymptotes of simple rational functions from their equations. Interpret a graph of a rational function and explain the meaning of the horizontal asymptote in context. Lesson 19 Calculate the end behavior of a rational function by rewriting it in the form \(f(x)=q(x)+\frac{r(x)}{b(x)}\). Generalize from specific rational functions to state relationships between the end behavior and the degrees of the numerator and denominator.
Rational Equations	Lesson 20 Calculate solutions to equations involving a single rational expression. Create simple equations involving a rational expression to solve a problem in context. Lesson 21 Create a simple equation involving two rational expressions to model a situation and use the model to answer questions. Use strategic multiplication to solve equations that have rational expressions on both sides. Lesson 22 Determine whether there are extraneous solutions to a rational equation. Explain (orally and in writing) how extraneous solutions can arise when solving rational equations.
Polynomial Identities	Lesson 23 Comprehend what a polynomial identity is. Prove some common identities. Lesson 24 Create expressions to represent a mathematical situation and justify an identity about them. Justify (in writing) general relationships by using identities. Lesson 25 Calculate sums of terms in a geometric sequence by using a formula. Understand the derivation of the formula for the sum of the first \(n\) terms in a finite geometric sequence. Lesson 26 Calculate solutions to problems by using the formula for the first \(n\) terms in a geometric sequence. Interpret results about geometric sums in non-mathematical contexts.

Alg2.2: Polynomials