# Polynomial Functions

**3.1 Graphing Polynomial Functions Using Transformations**

**Explanation****Practice Problems**Desmos Activity: Translation of Cubic Functions (teacher use)

**3.2 End Behavior of Polynomial Functions Given a Graph or Equation**

**Explanation:**Khan article: End behavior of polynomials

Khan video: Intro to end behavior of polynomials (8:09)

Khan video: End behavior of functions & their graphs (all content) (2:22)

**Practice Problems**Khan Exercise: End behavior of polynomials (all in standard form)

**3.3 Zeros of Polynomial Functions**

**Explanation**Khan video: Zeros of polynomials introduction (5:08)

Khan video: Zeros of polynomials: plotting zeros (3:18)

Khan video: Zeros of polynomials: matching equation to zeros (3:50)

Khan video: Zeros of polynomials: matching equation to graph (3:00)

Khan video: Zeros of polynomials (with factoring): grouping (4:54)

Khan video: Zeros of polynomials (with factoring): common factor (3:31)

Khan video: Factoring higher-degree polynomials (8:01)

**Practice Problems**Khan Exercise: Zeros of polynomials (factored form)

Khan Exercise: Zeros of polynomials (with factoring)

IXL: Algebra 2 L.8 Find the roots of factored polynomials

IXL: Algebra 2 L.9 Write a polynomial from its roots

IXL: Algebra 2: L.16 Fundamental Theorem of Algebra (honors)

**3.4 Real and Complex Roots**

Explanation:

Fundamental Theorem of Algebra

Complex conjugates

Rational Root Theorem: list the possible rational roots (a type of real roots)

Descartes' Rules of Signs: number of real positive and real negative roots

Practice Problems:

IXL: Algebra 2: L.10 Rational root theorem

IXL: Algebra 2: L.13 Descartes' Rule of Signs

**3.5 Positive/Negative Intervals of Polynomials and Multiplicity**

**Explanation:**Khan video: Increasing, decreasing, positive or negative intervals (Algebra 1) (5:55) - general understanding

Khan video: Worked example: positive & negative intervals (Algebra 1) (1:10) - general understanding

Khan video: Positive and negative intervals of polynomials (8:39)

Khan article: Positive & negative intervals of polynomials

Khan video: Multiplicity of zeros of polynomials (6:35)

Khan video: Zeros of polynomials (multiplicity) (4:59)

Khan article: Zeros of polynomials & their graphs

Khan article: Positive & negative intervals of polynomials

Khan article: Graphs of polynomials

Khan article: Graphs of polynomials: Challenge problems

**Practice problems:**Desmos Activity: Positive and Negative Intervals of a Function (teach use only)

Khan exercise: Positive and negative intervals (optional)

Khan Exercise: Positive & negative intervals of polynomials

Khan Exercise: Zeros of polynomials (multiplicity)

IXL: Algebra 2 L.14 Match polynomials and graphs (consider the end behavior, zeros, and y-intercepts)

**3.6 Increasing and Decreasing Intervals and Extrema **

**Explanation:**Khan video: Increasing, decreasing, positive or negative intervals (Algebra 1) (5:55; start the video at 2:34)

Khan video: Introduction to minimum and maximum points (Algebra 1) (5:29) uses more math symbols that are not necessary

Khan video: Worked example: absolute and relative extrema (Algebra 1) (4:57)

Khan video: Polynomial multiplication word problem (Algebra 1 - 2018) (4:18)

Khan video: Polynomial word problem: rectangle and circle area (Algebra 1 - 2018) (4:36)

Khan video: Polynomial word problem: total value of bills (Algebra 1 - 2018) (1:23)

Khan video: Polynomial word problem: area of a window (Algebra 1 - 2018) (4:47)

Khan video: Graph interpretation word problem: temperature

Khan video: Graph interpretation word problem: basketball

**Practice Problems:**Desmos Activity: Increasing/Decreasing Functions (teacher use only)

Khan exercise: Increasing and decreasing intervals (optional)

Khan exercise: Relative maxima and minima (Algebra 1)

Khan exercise: Absolute maxima and minima (Algebra 1)

Khan exercise: Graph interpretation word problems

Desmos Activity: Build a Bigger Field (teacher use only)

**3.7 Average Rate of Change**

**Explanation**Khan video: Introduction to average rate of change (Algebra 1) (5:30)

Khan video: Worked example: average rate of change from graph (Algebra 1) (2:14)

Khan video: Worked example: average rate of change from table (Algebra 1) (2:19)

Khan video: Average rate of change word problem: table (Algebra 1) (3:39)

Khan video: Average rate of change word problem: graph (Algebra 1) (6:57)

Khan article: Average rate of change review (Algebra 1)

Khan video: Average rate of change word problem: equation (Algebra 1 - 2018) (4:32)

Khan video: Finding average rate of change of polynomials (given an equation) (4:01)

**Practice Problems**IXL: Algebra 1 Q.17 Rate of change: graphs

Khan Exercise: Average rate of change word problems (Algebra 1)

Khan exercise: Average rate of change: graphs & tables (Algebra 1)

Khan Exercise: Average rate of change of polynomials

IXL: Algebra 1 Q.16 Rate of change: tables

IXL: Algebra 2 D.10 Average rate of change

**3.8 Symmetry of Functions **

**Explanation:**Khan video: Function symmetry introduction (5:21)

Khan article: Function symmetry introduction (Graphical)

Khan video: Even and odd functions: Graphs (3:52)

Khan video: Even and odd functions: Tables (Graphical) (4:08)

Khan video: Even & odd polynomials (equations) (Algebra 2 - 2018) (7:22)

Khan article: Symmetry of polynomials (Algebra 2 - 2018)

Khan article: Symmetry of algebraic models

**Practice Problems**Khan Exercise: Even and odd functions: Graphs and tables

Khan Exercise: Even & odd functions: Equations (Algebra 2 - 2018)

**3.9 Polynomial Division**

**Explanation**Math is Fun: Long Division (the website include text and animated explanations)

Khan video: Intro to long division of polynomials (12:08)

Khan video: Dividing polynomials by linear expressions (3:23)

Khan video: Dividing polynomials by linear expressions: missing term (4:31)

Khan video: Dividing polynomials with remainders (Algebra - all content: honors: dividing by a quadratic) (6:22)

Khan video: Intro to polynomial synthetic division (Algebra - all content) (5:20)

Khan video: Dividing polynomials: synthetic division (Algebra - all content) (4:59)

**Practice Problems**

Khan exercise: Divide quadratics by linear expressions (with remainders)

Khan exercise: Divide polynomials by linear expressions

**Teacher Resource**ExamView Test Bank (purchase)

**3.10 Factor Theorem and Remainder Theorem**

**Explanation**Khan video: Intro to factors & divisibility (Algebra 1) (5:25)

Khan article: Intro to factors & divisibility (Algebra 1)

Khan video: Factoring using polynomial division (completely factor) (5:57)

Khan video: Factoring using polynomial division: missing term (completely factor) (3:57)

Khan video: Intro to the Polynomial Remainder Theorem (6:42)

Khan video: Remainder theorem: finding remainder from equation (3:31)

Khan video: Remainder theorem examples (5:31)

Khan video: Using the Polynomial Remainder Theorem: checking factors (3:25)

**Practice Problems**Khan Exercise: Factor using polynomial division (Rewrite a function as a product of linear factors)

Khan exercise: Remainder theorem

Khan Exercise: Remainder theorem and factors

**Review**

**Explanation:****Practice Problems:**Desmos Class activity: Polygraph Polynomial

Desmos Activity: Match My Polynomial