Curriculum / Math / 11th Grade / Unit 3: Polynomials / Lesson 9
Math
Unit 3
11th Grade
Lesson 9 of 14
Jump To
Identify and factor with difference of two squares in quadratic and quartic polynomials. Describe identity of difference of two squares. Describe the zeros that represent the resultant factors.
The core standards covered in this lesson
A.APR.B.3 — 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.SSE.A.2 — Use the structure of an expression to identify ways to rewrite it. For example, see x<sup>4</sup> — y<sup>4</sup> as (x²)² — (y²)², thus recognizing it as a difference of squares that can be factored as (x² — y²)(x² + y²).
The foundational standards covered in this lesson
F.IF.C.8.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.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.
Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Find the zeros of the function$${f(x)=x^3-9x}$$.
Solving a Simple Cubic Equation, accessed on Sept. 25, 2017, 2 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
What are all of the linear factors of $${2x^4-162}$$? How would you write this expression in factored form?
How are the roots of a sum of two squares, such as $${x^2+9}$$, different from the roots of a difference of two squares?
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
How do the following problems represent differences of two squares? Factor to show the relationships.
$${4x^4-1}$$
$${x^{10}-36}$$
Factor the following functions and name all of the real and complex zeros.
$${18x^4-32}$$
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
Lesson 8
Lesson 10
Topic A: Polynomial Features and Graphs
Classify polynomials through identification of degree and leading coefficient. Graph a polynomial function from a table of values; prove degree using successive differences.
A.APR.A.1 F.IF.C.7.C F.IF.C.9
Identify features of polynomial functions including end behavior, intervals where the function is positive or negative, and domain and range of function.
F.BF.B.3 F.IF.B.4 F.IF.B.6 F.LE.A.3
Match and compare equations and graphs of polynomials, and identify transformations.
F.BF.B.3 F.IF.B.4 F.IF.C.7.C
Sketch polynomial functions using sign charts and analysis of the factored form of the polynomial function.Â
A.APR.B.3
Create a free account to access thousands of lesson plans.
Already have an account? Sign In
Topic B: Operations with Polynomials
Multiply polynomials, identifying factors, degrees, and number of real roots. Identify features of a polynomial in standard form.
A.APR.A.1 F.BF.B.3
Add and subtract polynomials. Identify degree, leading coefficient, and end behavior of result.
A.APR.A.1 F.BF.A.1.B
Divide polynomials by binomials to determine linear factors.
A.APR.A.1 A.APR.B.2 A.APR.B.3
Determine if a binomial is a factor of a polynomial using the remainder theorem.
A.APR.B.2
A.APR.B.3 A.SSE.A.2
Factor difference and sums of cubes. Explain sums and differences of cubes as polynomial identities.
A.APR.C.4
Factor polynomials by grouping in quartic, cubic, and quadratic functions.
F.IF.C.8.A
Topic C: Polynomial Extensions
Use polynomial identities to determine Pythagorean triples.
Identify the solution(s) to systems of polynomial functions.
A.REI.D.11
2 days
Write polynomial functions from solutions of that polynomial function.
See all of the features of Fishtank in action and begin the conversation about adoption.
Learn more about Fishtank Learning School Adoption.
Yes
No
Access rigorous, relevant, and adaptable math lesson plans for free