HSA-APR.C.4
Scroll Up
- HSA-APR.C.4Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x^{2} + y^{2})^{2} = (x^{2} - y^{2})^{2} + (2xy)^{2} can be used to generate Pythagorean triples.
- HSA-APR.C.5(+) Know and apply the Binomial Theorem for the expansion of (x + y)^{n} in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascalâ€™s Triangle.
Scroll Down
HSA-APR.C.4
Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x^{2} + y^{2})^{2} = (x^{2} - y^{2})^{2} + (2xy)^{2} can be used to generate Pythagorean triples.
29 Lesson(s)
Proving Polynomial Identities
Algebra II »
Unit: Polynomial Theorems and Graphs
Algebra II »
Unit: Polynomial Theorems and Graphs
Big Idea:
There are links between polynomials and geometry. Both branches of math use proof and a polynomial identity can be used to generate Pythagorean triples.
Standards:
Favorites
(5)
Resources
(18)
Reflections
(1)
Review of Polynomial Roots and Complex Numbers
Algebra II »
Unit: Polynomial Theorems and Graphs
Algebra II »
Unit: Polynomial Theorems and Graphs
Big Idea:
Arithmetic with polynomials and complex numbers are performed in similar ways, but powers of i have a meaning distinct from powers of variables.
Standards:
Favorites
(2)
Resources
(10)
The Remainder Theorem
Algebra II »
Unit: Polynomial Theorems and Graphs
Algebra II »
Unit: Polynomial Theorems and Graphs
Big Idea:
Any polynomial p(x) can be written as a product of (x – a) and some quotient q(x), plus the remainder p(a).
Standards:
Favorites
(4)
Resources
(13)
Reflections
(1)
Quiz and Intro to Graphs of Polynomials
Algebra II »
Unit: Polynomial Theorems and Graphs
Algebra II »
Unit: Polynomial Theorems and Graphs
Big Idea:
The graph of a polynomial can look a variety of ways depending on the degree, lead coefficient, and linear factors.
Standards:
Favorites
(3)
Resources
(12)
Reflections
(1)
Seeing Structure in Expressions - Factoring Higher Order Polynomials
Algebra II »
Unit: Polynomial Theorems and Graphs
Algebra II »
Unit: Polynomial Theorems and Graphs
Big Idea:
Like quadratic expressions, some higher order polynomial expressions can be rewritten in factored form to reveal values that make the expression equal to zero.
Standards:
Favorites
(5)
Resources
(25)
Reflections
(2)
Polynomial Long Division and Solving Polynomial Equations
Algebra II »
Unit: Polynomial Theorems and Graphs
Algebra II »
Unit: Polynomial Theorems and Graphs
Big Idea:
Operations with polynomials are a lot like operations with integers.
Standards:
Favorites
(6)
Resources
(22)
Reflections
(1)
The Fundamental Theorem of Algebra and Imaginary Solutions
Algebra II »
Unit: Polynomial Theorems and Graphs
Algebra II »
Unit: Polynomial Theorems and Graphs
Big Idea:
The degree of a polynomial equation tells us how many solutions to expect as long as we include both real and imaginary solutions.
Standards:
Resources
(14)
Reflections
(1)
Arithmetic with Complex Numbers
Algebra II »
Unit: Polynomial Theorems and Graphs
Algebra II »
Unit: Polynomial Theorems and Graphs
Big Idea:
Imaginary numbers are used to represent quantities that have two parts; working with these numbers is similar to working with polynomial expressions.
Standards:
Favorites
(5)
Resources
(23)
Reflections
(2)
Unit Test: Sequences and Series
Algebra II »
Unit: Sequences and Series
Algebra II »
Unit: Sequences and Series
Performance Task - Representing Polynomials
Algebra II »
Unit: Polynomial Theorems and Graphs
Algebra II »
Unit: Polynomial Theorems and Graphs
Big Idea:
The graphs of polynomial functions can be transformed by altering the algebraic form in specific ways. These transformations have the same effect on all the function types studied in Algebra 2 and Precalculus.
Standards:
Favorites
(2)
Resources
(15)
Reflections
(1)
Graphing Polynomials - End Behavior
Algebra II »
Unit: Polynomial Theorems and Graphs
Algebra II »
Unit: Polynomial Theorems and Graphs
Big Idea:
A good sketch of a polynomial function can be produced by considering the end-behavior, roots and y-intercept of a polynomial function.
Standards:
Favorites
(7)
Resources
(15)
Reflections
(1)
Big Idea:
Show your students that they really can "prove it" with this lesson on polynomial identities.
Standards:
Favorites
(1)
Resources
(10)
Reflections
(1)
Big Idea:
First you create it, then you use it...this lesson allows students to use the polynomial identities they just proved.
Standards:
Resources
(14)
Reflections
(1)
Graphing Polynomials - Roots and the Fundamental Theorem of Algebra
Algebra II »
Unit: Polynomial Theorems and Graphs
Algebra II »
Unit: Polynomial Theorems and Graphs
Big Idea:
A good sketch of a polynomial function can be produced by considering the end-behavior, roots and y-intercept of a polynomial function.
Standards:
Favorites
(6)
Resources
(20)
Reflections
(1)
Big Idea:
Egyptian fractions provide an interesting arena for putting rational functions to use.
Standards:
Resources
(9)
Common Core Math
Kindergarten
First Grade
Second Grade
Third Grade
Fourth Grade
Fifth Grade
Sixth Grade
Seventh Grade
HS Number & Quantity
HS Algebra
HS Functions
HS Geometry
Kindergarten
First Grade
Second Grade
Third Grade
Fourth Grade
Fifth Grade
Sixth Grade
Seventh Grade
Eighth Grade
Ninth and Tenth Grade
Kindergarten
First grade
Second grade
Third Grade
Fourth grade
Fifth grade
Middle School
Kindergarten
First Grade
Second Grade
Third Grade
Fourth Grade
Fifth Grade
Sixth Grade
Seventh Grade
HS Number & Quantity
HS Algebra
HS Functions
HS Geometry
Kindergarten
First Grade
Second Grade
Third Grade
Fourth Grade
Fifth Grade
Sixth Grade
Seventh Grade
Eighth Grade
Ninth and Tenth Grade
Kindergarten
First grade
Second grade
Third Grade
Fourth grade
Fifth grade
Middle School