ALEX Classroom Resources

ALEX Classroom Resources  
   View Standards     Standard(s): [MA2015] AL1 (9-12) 32 :
32 ) Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. [F-IF8]

a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. [F-IF8a]

b. Use the properties of exponents to interpret expressions for exponential functions. [F-IF8b]

Example: Identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, and y = (1.2)t/10, and classify them as representing exponential growth and decay.

[MA2015] AL2 (9-12) 4 :
4 ) Solve quadratic equations with real coefficients that have complex solutions. [N-CN7]

[MA2015] AL2 (9-12) 13 :
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).

[MA2015] ALT (9-12) 4 :
4 ) Solve quadratic equations with real coefficients that have complex solutions. [N-CN7]

[MA2015] ALT (9-12) 13 :
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).

[MA2019] AL1-19 (9-12) 5 :
5. Use the structure of an expression to identify ways to rewrite it.

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).
[MA2019] AL1-19 (9-12) 6 :
6. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

a. Factor quadratic expressions with leading coefficients of one, and use the factored form to reveal the zeros of the function it defines.

b. Use the vertex form of a quadratic expression to reveal the maximum or minimum value and the axis of symmetry of the function it defines; complete the square to find the vertex form of quadratics with a leading coefficient of one.

c. Use the properties of exponents to transform expressions for exponential functions.

Example: Identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t/10, and classify them as representing exponential growth or decay.
[MA2019] AL1-19 (9-12) 9 :
9. Select an appropriate method to solve a quadratic equation in one variable.

a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)2 = q that has the same solutions. Explain how the quadratic formula is derived from this form.

b. Solve quadratic equations by inspection (such as x2 = 49), taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation, and recognize that some solutions may not be real.
Subject: Mathematics (9 - 12), Mathematics (9 - 12)
Title: Rewriting Quadratic Expressions in Factored Form (Part 1): Algebra 1, Episode 15: Unit 7, Lesson 6 | Illustrative Math
URL: https://aptv.pbslearningmedia.org/resource/im20-math-ep15-76/rewriting-quadratic-expressions-in-factored-form-part-1/
Description:

In this video lesson, students begin to rewrite quadratic expressions from standard to factored form.

Students relate the numbers in the factored form to the coefficients of the terms in standard form, looking for a structure that can be used to go in reverse—from standard form to factored form (MP7).

(This lesson only looks at expressions of the form (x + m)(x + n) and (x – m)(x – n) where m and n are positive.)



   View Standards     Standard(s): [MA2015] AL1 (9-12) 32 :
32 ) Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. [F-IF8]

a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. [F-IF8a]

b. Use the properties of exponents to interpret expressions for exponential functions. [F-IF8b]

Example: Identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, and y = (1.2)t/10, and classify them as representing exponential growth and decay.

[MA2015] AL2 (9-12) 4 :
4 ) Solve quadratic equations with real coefficients that have complex solutions. [N-CN7]

[MA2015] AL2 (9-12) 13 :
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).

[MA2015] ALT (9-12) 4 :
4 ) Solve quadratic equations with real coefficients that have complex solutions. [N-CN7]

[MA2015] ALT (9-12) 13 :
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).

[MA2019] AL1-19 (9-12) 5 :
5. Use the structure of an expression to identify ways to rewrite it.

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).
[MA2019] AL1-19 (9-12) 6 :
6. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

a. Factor quadratic expressions with leading coefficients of one, and use the factored form to reveal the zeros of the function it defines.

b. Use the vertex form of a quadratic expression to reveal the maximum or minimum value and the axis of symmetry of the function it defines; complete the square to find the vertex form of quadratics with a leading coefficient of one.

c. Use the properties of exponents to transform expressions for exponential functions.

Example: Identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t/10, and classify them as representing exponential growth or decay.
[MA2019] AL1-19 (9-12) 9 :
9. Select an appropriate method to solve a quadratic equation in one variable.

a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)2 = q that has the same solutions. Explain how the quadratic formula is derived from this form.

b. Solve quadratic equations by inspection (such as x2 = 49), taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation, and recognize that some solutions may not be real.
Subject: Mathematics (9 - 12), Mathematics (9 - 12)
Title: Rewriting Quadratic Expressions in Factored Form (Part 2): Algebra 1, Episode 16: Unit 7, Lesson 7 | Illustrative Math
URL: https://aptv.pbslearningmedia.org/resource/im20-math-ep16-77/rewriting-quadratic-expressions-in-factored-form-part-2/
Description:

Earlier in this video series, students transformed quadratic expressions from standard form into factored form. There, the factored expressions are products of two sums, (x + m)(x + n), or two differences, (x – m)(x – n). Students continue that work in this video lesson, extending it to include expressions that can be rewritten as products of a sum and a difference, (x + m)(x – n).

Through repeated reasoning, students notice that when we apply the distributive property to multiply out a sum and a difference, the product has a negative constant term, but the linear term can be negative or positive (MP8). Students make use of the structure as they take this insight to transform quadratic expressions into factored form (MP7).



   View Standards     Standard(s): [MA2015] AL1 (9-12) 32 :
32 ) Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. [F-IF8]

a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. [F-IF8a]

b. Use the properties of exponents to interpret expressions for exponential functions. [F-IF8b]

Example: Identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, and y = (1.2)t/10, and classify them as representing exponential growth and decay.

[MA2015] AL2 (9-12) 4 :
4 ) Solve quadratic equations with real coefficients that have complex solutions. [N-CN7]

[MA2015] AL2 (9-12) 13 :
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).

[MA2015] ALT (9-12) 4 :
4 ) Solve quadratic equations with real coefficients that have complex solutions. [N-CN7]

[MA2015] ALT (9-12) 13 :
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).

[MA2019] AL1-19 (9-12) 5 :
5. Use the structure of an expression to identify ways to rewrite it.

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).
[MA2019] AL1-19 (9-12) 6 :
6. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

a. Factor quadratic expressions with leading coefficients of one, and use the factored form to reveal the zeros of the function it defines.

b. Use the vertex form of a quadratic expression to reveal the maximum or minimum value and the axis of symmetry of the function it defines; complete the square to find the vertex form of quadratics with a leading coefficient of one.

c. Use the properties of exponents to transform expressions for exponential functions.

Example: Identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t/10, and classify them as representing exponential growth or decay.
[MA2019] AL1-19 (9-12) 9 :
9. Select an appropriate method to solve a quadratic equation in one variable.

a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)2 = q that has the same solutions. Explain how the quadratic formula is derived from this form.

b. Solve quadratic equations by inspection (such as x2 = 49), taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation, and recognize that some solutions may not be real.
Subject: Mathematics (9 - 12), Mathematics (9 - 12)
Title: Rewriting Quadratic Expressions in Factored Form (Part 3): Algebra 1, Episode 17: Unit 7, Lesson 8 | Illustrative Math
URL: https://aptv.pbslearningmedia.org/resource/im20-math-ep17-78/rewriting-quadratic-expressions-in-factored-form-part-3/
Description:

In this video lesson, students encounter quadratic expressions without a linear term and consider how to write them in factored form.

Through repeated reasoning, students are able to generalize the equivalence of these two forms: (x + m)(x – m) and x2 – m2 (MP8). Then, they make use of the structure relating the two expressions to rewrite expressions (MP7) from one form to the other.

Students also consider why a difference of two squares (such as x2 – 25) can be written in factored form, but a sum of two squares (such as x2 + 25) cannot be, even though both are quadratic expressions with no linear term.



   View Standards     Standard(s): [MA2015] AL2 (9-12) 4 :
4 ) Solve quadratic equations with real coefficients that have complex solutions. [N-CN7]

[MA2015] AL2 (9-12) 13 :
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).

[MA2015] ALT (9-12) 4 :
4 ) Solve quadratic equations with real coefficients that have complex solutions. [N-CN7]

[MA2015] ALT (9-12) 13 :
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).

[MA2019] AL1-19 (9-12) 5 :
5. Use the structure of an expression to identify ways to rewrite it.

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).
[MA2019] AL1-19 (9-12) 6 :
6. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

a. Factor quadratic expressions with leading coefficients of one, and use the factored form to reveal the zeros of the function it defines.

b. Use the vertex form of a quadratic expression to reveal the maximum or minimum value and the axis of symmetry of the function it defines; complete the square to find the vertex form of quadratics with a leading coefficient of one.

c. Use the properties of exponents to transform expressions for exponential functions.

Example: Identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t/10, and classify them as representing exponential growth or decay.
[MA2019] AL1-19 (9-12) 9 :
9. Select an appropriate method to solve a quadratic equation in one variable.

a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)2 = q that has the same solutions. Explain how the quadratic formula is derived from this form.

b. Solve quadratic equations by inspection (such as x2 = 49), taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation, and recognize that some solutions may not be real.
Subject: Mathematics (9 - 12), Mathematics (9 - 12)
Title: What Are Perfect Squares?: Algebra 1, Episode 19: Unit 7, Lesson 11 | Illustrative Math
URL: https://aptv.pbslearningmedia.org/resource/im20-math-ep19-711/what-are-perfect-squares/
Description:

This video lesson has two key aims. The first aim is to familiarize students with the structure of perfect-square expressions. Students analyze various examples of perfect squares. They apply the distributive property repeatedly to expand perfect-square expressions given in the factored form (MP8). The repeated reasoning allows them to generalize expressions of the form (x + n)2 as equivalent to x2 + 2nx + n2.

The second aim is to help students see that perfect squares can be handy for solving equations because we can find their square roots. Recognizing the structure of a perfect square equips students to look for features that are necessary to complete a square (MP7), which they will do in a future video lesson.



   View Standards     Standard(s): [MA2015] AL2 (9-12) 13 :
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).

[MA2015] ALT (9-12) 13 :
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).

[MA2019] AL1-19 (9-12) 5 :
5. Use the structure of an expression to identify ways to rewrite it.

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).
[MA2019] AL1-19 (9-12) 6 :
6. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

a. Factor quadratic expressions with leading coefficients of one, and use the factored form to reveal the zeros of the function it defines.

b. Use the vertex form of a quadratic expression to reveal the maximum or minimum value and the axis of symmetry of the function it defines; complete the square to find the vertex form of quadratics with a leading coefficient of one.

c. Use the properties of exponents to transform expressions for exponential functions.

Example: Identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t/10, and classify them as representing exponential growth or decay.
Subject: Mathematics (9 - 12), Mathematics (9 - 12)
Title: Standard Form and Factored Form: Algebra 1, Episode 8: Unit 6, Lesson 9 | Illustrative Math
URL: https://aptv.pbslearningmedia.org/resource/im20-math-ep8-69/standard-form-and-factored-form/
Description:

Previously in this video series, students used area diagrams to expand expressions of the form (x + p)(x + q) and generalized that the expanded expressions take the form of x2 + (p + q)x + pq. In this video lesson, they see that the same generalization can be applied when the factored expression contains a sum and a difference (when p or q is negative) or two differences (when both p and q are negative).

Students transition from thinking about rectangular diagrams concretely, in terms of area, to thinking about them more abstractly, as a way to organize the terms in each factor. They also learn to use the terms standard form and factored form. When classifying quadratic expressions by their form, students refine their language and thinking about quadratic expressions (MP6).



   View Standards     Standard(s): [MA2015] AL1 (9-12) 16 :
16 ) Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. [A-REI1]

[MA2015] AL1 (9-12) 17 :
17 ) Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. [A-REI3]

[MA2015] AL2 (9-12) 4 :
4 ) Solve quadratic equations with real coefficients that have complex solutions. [N-CN7]

[MA2015] AL2 (9-12) 13 :
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).

[MA2015] AL2 (9-12) 20 :
20 ) Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. [A-CED1]

[MA2015] AL2 (9-12) 24 :
24 ) Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. [A-REI2]

[MA2015] AL2 (9-12) 29 :
29 ) Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [F-IF5]

Example: If the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.

[MA2015] ALT (9-12) 4 :
4 ) Solve quadratic equations with real coefficients that have complex solutions. [N-CN7]

[MA2015] ALT (9-12) 13 :
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).

[MA2015] ALT (9-12) 20 :
20 ) Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. [A-CED1]

[MA2015] ALT (9-12) 24 :
24 ) Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. [A-REI2]

[MA2015] ALT (9-12) 29 :
29 ) Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [F-IF5]

Example: If the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.

[MA2019] AL1-19 (9-12) 5 :
5. Use the structure of an expression to identify ways to rewrite it.

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).
[MA2019] AL1-19 (9-12) 6 :
6. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

a. Factor quadratic expressions with leading coefficients of one, and use the factored form to reveal the zeros of the function it defines.

b. Use the vertex form of a quadratic expression to reveal the maximum or minimum value and the axis of symmetry of the function it defines; complete the square to find the vertex form of quadratics with a leading coefficient of one.

c. Use the properties of exponents to transform expressions for exponential functions.

Example: Identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t/10, and classify them as representing exponential growth or decay.
[MA2019] AL1-19 (9-12) 9 :
9. Select an appropriate method to solve a quadratic equation in one variable.

a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)2 = q that has the same solutions. Explain how the quadratic formula is derived from this form.

b. Solve quadratic equations by inspection (such as x2 = 49), taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation, and recognize that some solutions may not be real.
[MA2019] AL1-19 (9-12) 11 :
11. Create equations and inequalities in one variable and use them to solve problems in context, either exactly or approximately. Extend from contexts arising from linear functions to those involving quadratic, exponential, and absolute value functions.
[MA2019] AL1-19 (9-12) 15 :
15. Define a function as a mapping from one set (called the domain) to another set (called the range) that assigns to each element of the domain exactly one element of the range.

a. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Note: If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x.

b. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Limit to linear, quadratic, exponential, and absolute value functions.
Subject: Mathematics (9 - 12), Mathematics (9 - 12)
Title: Applying the Quadratic Formula (Part 1): Algebra 1, Episode 24: Unit 7, Lesson 17 | Illustrative Math
URL: https://aptv.pbslearningmedia.org/resource/im20-math-ep24-717/applying-the-quadratic-formula-part-1/
Description:

In this video lesson, students return to some quadratic functions they have seen. They write quadratic equations to represent relationships and use the quadratic formula to solve problems that they did not previously have the tools to solve (other than by graphing). In some cases, the quadratic formula is the only practical way to find the solutions. In others, students can decide to use other methods that might be more straightforward (MP5).

The work in this lesson—writing equations, solving them, and interpreting the solutions in context—encourages students to reason quantitatively and abstractly (MP2).



   View Standards     Standard(s): [MA2015] AL2 (9-12) 13 :
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).

[MA2015] AL2 (9-12) 18 :
18 ) Prove polynomial identities and use them to describe numerical relationships. [A-APR4]

Example: The polynomial identity (x2 + y2)2 = (x2 - y2)2 + (2xy)2 can be used to generate Pythagorean triples.

Subject: Mathematics (9 - 12)
Title: Algebra II Module 1, Topic A: Polynomials--From Base 10 to Base X
URL: https://www.engageny.org/resource/algebra-ii-module-1-topic-a-overview
Description:

The focus in Module 1, Topic A is on polynomial arithmetic and how it is analogous to operations with integers. The module opens with a lively lesson that engages students in writing polynomial expressions for sequences by examining successive differences. Later in this topic, students gain fluency with polynomial operations and work with identities such as a2-b2=(a+b)(a-b). The topic closes with an emphasis on the use of factoring and the special role of zeros when solving polynomial equations.



   View Standards     Standard(s): [MA2015] AL2 (9-12) 13 :
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).

[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.
Subject: Mathematics (9 - 12), Mathematics (9 - 12)
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
Description:

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.  



ALEX Classroom Resources: 8

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