Unit 3 - polynomial functions
In this unit, students continue their study of polynomials by identifying zeros and making connections between zeros of a polynomial and solutions of a polynomial equation. Students will see how the Fundamental Theorem of Algebra can be used to determine the number of solutions of a polynomial equation and will find all the roots of those equations. Students will graph polynomial functions and interpret the key characteristics of the function.
MGSE9-12.N.CN.9 Use the Fundamental Theorem of Algebra to find all roots of a polynomial equation Interpret the structure of expressions
MGSE9-12.A.SSE.1 Interpret expressions that represent a quantity in terms of its context.
MGSE9-12.A.SSE.1a Interpret parts of an expression, such as terms, factors, and coefficients, in context.
MGSE9-12.A.SSE.1b Given situations which utilize formulas or expressions with multiple terms and/or factors, interpret the meaning (in context) of individual terms or factors.
MGSE9-12.A.SSE.2 Use the structure of an expression to rewrite it in different equivalent forms. For example, see x^4 – y^4 as (x^2)^2 - (y^2)^2 , thus recognizing it as a difference of squares that can be factored as (x^2 – y^2 )(x^2 + y^2 ).
MGSE9-12.A.SSE.1 Interpret expressions that represent a quantity in terms of its context.
MGSE9-12.A.SSE.1a Interpret parts of an expression, such as terms, factors, and coefficients, in context.
MGSE9-12.A.SSE.1b Given situations which utilize formulas or expressions with multiple terms and/or factors, interpret the meaning (in context) of individual terms or factors.
MGSE9-12.A.SSE.2 Use the structure of an expression to rewrite it in different equivalent forms. For example, see x^4 – y^4 as (x^2)^2 - (y^2)^2 , thus recognizing it as a difference of squares that can be factored as (x^2 – y^2 )(x^2 + y^2 ).
Explanation of Fundamental Theorem of Algebra
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Polynomial root calculator
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What is factoring?
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ck12
When do I know if a number is a factor?
Improve your divisibility skills practice...
Pre-factoring for roots of polynomials
Factor these 10! You will used a variety of factoring strageties.
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Roots, zeros, factors, etc. explained
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Rational Zeros Theorem explained
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FToA focus real, imag, real + imag, multiplicity...after an explanation, we will work on 1-10 at the bottom of website.
HO Graphing basics linear through quantic, and a few more important things
Given roots/zeros/solutions find the polynomials
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Kahn explanation of FToA
We will look at some of these examples...
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Please view the following video to learn where to look for the intervals of increase and decrease, also the maximum/s and minimum/s of polynomial graphs
Try your characteristic skills on various polynomial graphs
A little random polynomial practice
Proving polynomial identities
Kahn's identity practice
Pythagorean triples
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What is a polynomial identity
Regents exam
Mathisfun
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Find one out of state college/university you might be interested in attending & enter your research in the correct columns on the following google doc on the website
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There are 30 practice problems at the following url on the website, please get busy
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Mixed practice on Unit 3 = Any practice from Section 2, Section 3 or Section 4
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