Curriculum / Math / 11th Grade / Unit 3: Polynomials / Lesson 8
Math
Unit 3
11th Grade
Lesson 8 of 14
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Determine if a binomial is a factor of a polynomial using the remainder theorem.
The core standards covered in this lesson
A.APR.B.2 — 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).
The foundational standards covered in this lesson
A.REI.D.10 — Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Which of the following binomials are factors of the polynomial? Explain your reasoning.
$${x^4+5x^3-x^2-17x+12}$$
$${(x-1) }$$ $${(x+1)}$$ $${(x+3)}$$ $${(x+5)}$$ $${(x+4)}$$ $${(x-2)}$$
What is the value of a in the polynomial shown below if $${x+2}$$ is a factor of that polynomial?
$${3x^4+6x^3+ax^2+3x+9}$$
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Is $${x+1}$$Â a factor of $${2x^2-3x-5}$$? How do you know? Show your reasoning using long division and by using the value of $$x$$Â at the root.
Algebra II > Module 1 > Topic A > Lesson 4 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..
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 7
Lesson 9
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
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
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.
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