Curriculum / Math / 11th Grade / Unit 3: Polynomials / Lesson 11
Math
Unit 3
11th Grade
Lesson 11 of 14
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Factor polynomials by grouping in quartic, cubic, and quadratic functions.
The core 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 foundational standards covered in this lesson
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 essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
We will not be using the rational roots theorem, so ensure that the problems you provide are factorable using one of the methods determined in this unit so far.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Find the roots of the function $${f(x)=9x^3+36x^2-4x-16}$$.
Find the roots of the function $${g(x)=x^4-x^2-12}$$.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Find all of the roots of the following quartic equation:Â
$${h(x)=x^4-2x^3-9x^2-18x}$$
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 10
Lesson 12
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
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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
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.
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
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.
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