Lesson 9 | Polynomials | 11th Grade Mathematics

Objective

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.

Lesson Map

Topic A: Polynomial Features and Graphs

Lesson

Classify polynomials through identification of degree and leading coefficient. Graph a polynomial function from a table of values; prove degree using successive differences.

Standards

A.APR.A.1F.IF.C.7.CF.IF.C.9

Lesson

Identify features of polynomial functions including end behavior, intervals where the function is positive or negative, and domain and range of function.

Standards

F.BF.B.3F.IF.B.4F.IF.B.6F.LE.A.3

Lesson

Match and compare equations and graphs of polynomials, and identify transformations.

Standards

F.BF.B.3F.IF.B.4F.IF.C.7.C

Lesson

Sketch polynomial functions using sign charts and analysis of the factored form of the polynomial function.

Standards

A.APR.B.3

Topic B: Operations with Polynomials

Lesson

Multiply polynomials, identifying factors, degrees, and number of real roots. Identify features of a polynomial in standard form.

Standards

A.APR.A.1F.BF.B.3

Lesson

Add and subtract polynomials. Identify degree, leading coefficient, and end behavior of result.

Standards

A.APR.A.1F.BF.A.1.B

Lesson

Divide polynomials by binomials to determine linear factors.

Standards

A.APR.A.1A.APR.B.2A.APR.B.3

Lesson

Determine if a binomial is a factor of a polynomial using the remainder theorem.

Standards

A.APR.B.2

Lesson

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.

Standards

A.APR.B.3A.SSE.A.2

Lesson

Factor difference and sums of cubes. Explain sums and differences of cubes as polynomial identities.

Standards

A.APR.C.4

Lesson

Factor polynomials by grouping in quartic, cubic, and quadratic functions.

Standards

F.IF.C.8.A

Topic C: Polynomial Extensions

Lesson

Use polynomial identities to determine Pythagorean triples.

Standards

A.APR.C.4

Lesson

Identify the solution(s) to systems of polynomial functions.

Standards

A.REI.D.11

Lesson

2 days

Write polynomial functions from solutions of that polynomial function.

Standards

A.APR.B.3

Polynomials

Objective

Lesson Map

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Polynomials

Objective

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