Unit 2: Polynomial Functions

Students extend their work with linear and quadratic functions to polynomials of higher degree, moving flexibly between standard and factored forms, sketching graphs from key features (zeros, multiplicity, end behavior), and dividing polynomials to apply the Remainder Theorem.

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Unit

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Concept

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Practice

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Set 1

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Set 2

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Advanced

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Set 2

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What this unit covers

A What Is a Polynomial? · 4 lessons

Goals

• Generalize that when polynomials are combined by addition, subtraction, or multiplication, the result is a polynomial.
• Identify and interpret relative minimums, relative maximums, the degree, and the constant term of polynomials and their graphs.

Lessons

1. Let’s Make a Box
2. Funding the Future
3. Introducing Polynomials
4. Combining Polynomials

B Working with Polynomials · 3 lessons

Goals

• Determine properties of polynomials by representing them in standard or factored form.
• Generate a possible expression for a polynomial function given the horizontal intercepts of the function.
• Identify zeros of polynomial functions written in factored form.

Lessons

1. Connecting Factors and Zeros
2. Different Forms
3. Using Factors and Zeros

C Graphs of Polynomials · 4 lessons

Goals

• Calculate the solution to a system of polynomial equations.
• Create equations for polynomial functions with specific end behavior.
• Use zeros and multiplicities to sketch a graph of a polynomial function given in factored form.

Lessons

1. End Behavior (Part 1)
2. End Behavior (Part 2)
3. Multiplicity
4. Finding Intersections

D Polynomial Division · 4 lessons

Goals

• Generalize that for a polynomial and a number c, the remainder on division by (x − c) is the value of the polynomial at c.
• Rewrite a polynomial as the product of linear factors.

Lessons

1. Polynomial Division (Part 1)
2. Polynomial Division (Part 2)
3. What Do You Know about Polynomials?
4. The Remainder Theorem