Module 4

Polynomial Functions

Click on the section heading to find notes, homework and additional resources!

4.1 Intro to Polynomials

I can perform operations on polynomial functions
I classify a polynomial by the degree and number of terms

4.2 Graphing Polynomials

I can graph the parent function of polynomials up to the fifth degree
I can predict the end behavior of a polynomial function
I can find the turning points of a polynomial function using a calculator

4.3 Roots of Polynomials

I can find the zeroes of a polynomial equation by graphing
I can state the multiplicity of solution given the factors of a polynomial

4.4 Factoring Polynomials

I can factor a GCF out of a polynomial
I can fully factor a polynomial using the difference of squares
I can fully factor a polynomial using the difference of cubes
I can fully factor a polynomial using the sum of cubes
I can fully factor a trinomial using the "AC Method"
I can fully factor a polynomial using the grouping method

4.5 Dividing Polynomials

I can divide a polynomial by a monomial
I can perform long division to find the quotient of a polynomial and a binomial
I can utilize synthetic division to find the quotient of a polynomial and a binomial

Snow White & the "polyGNOMials"

State Standards:

A.APR.B.3: Know and use polynomial identities to describe numerical relationships
A.SSA.A.1: Use the structure of an expression to identify ways to rewrite it
A.CED.A.2: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations
A.APR.A.1 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).
A.APR.A.2 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough draft of the function defined by the polynomial.
F.IF.A.1 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. ★
F.IF.A.2 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. ★
F.IF.B.3 Graph functions expressed symbolically and show key features of the graph, by hand and using technology. ★
F.IF.B.5 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
A.REI.D.6 Explain why the x-coordinates of the points where the graphs of the equations y=f(x) and y=g(x) intersect are the solutions of the equation f(x)=g(x); find the approximate solutions using technology. ★
F.BF.A.1 Write a function that describes a relationship
S.ID.B.2 Represent data on two quantitative variables on a scatter plot and describe how the variables are related.

Report abuse