For the minimal polynomial of an algebraic element of a field, see Minimal polynomial (field theory).  In linear algebra, the minimal polynomial μA of an n × n matrix A over a field F is the monic polynomial P over F of least degree such that P(A) = 0. Any other polynomial Q with Q(A) = 0 is a (polynomial) multiple of μA.  The following three statements are equivalent:      λ is a root of μA,     λ is a root of the characteristic polynomial χA of A,     λ is an eigenvalue of matrix A.  The…

For the minimal polynomial of an algebraic element of a field, see Minimal polynomial (field theory). In linear algebra, the minimal polynomial μA of an n × n matrix A over a field F is the monic polynomial P over F of least degree such that P(A) = 0. Any other polynomial Q with Q(A) = 0 is a (polynomial) multiple of μA. The following three statements are equivalent: λ is a root of μA, λ is a root of the characteristic polynomial χA of A, λ is an eigenvalue of matrix A. The…

Example of finding the characteristic polynomial and its factorization in a Diagonalization problem.

Example of finding the characteristic polynomial and its factorization in a Diagonalization problem.

Students will find all zeros of 10 different polynomial functions. They will then match their answer to a characteristic of the snowman and color him correctly. Students should be able to solve equations, use synthetic division, use the quadratic formula, and solve problems using imaginary numbers.

Snowman Math Zeros of Polynomial Functions

Students will find all zeros of 10 different polynomial functions. They will then match their answer to a characteristic of the snowman and color him correctly. Students should be able to solve equations, use synthetic division, use the quadratic formula, and solve problems using imaginary numbers.

Characteristics of Parabolas Interactive Notebook Page - quadratic function inb page

Characteristics of Parabolas Interactive Notebook Page - quadratic function inb page

Do you ever get the question: "How does this math apply to real-life?" When you cover the unit on the Characteristics of Polynomials you can provide a true representation of a real-life scenario for the students to apply their teachings. Students will be able to gain not only a deeper understanding of interpreting a graph, but how it applies to the construction of a real roller coaster that they have seen at any amusement park. The students will work together to create their own unique…

Do you ever get the question: "How does this math apply to real-life?" When you cover the unit on the Characteristics of Polynomials you can provide a true representation of a real-life scenario for the students to apply their teachings. Students will be able to gain not only a deeper understanding of interpreting a graph, but how it applies to the construction of a real roller coaster that they have seen at any amusement park. The students will work together to create their own unique…

My Algebra 2 students rocked their summative activity on increasing and decreasing intervals!

Increasing and Decreasing Functions Activity

My Algebra 2 students rocked their summative activity on increasing and decreasing intervals!

A Heuristic Quasi-Polynomial Algorithm for Discrete Logarithm in Finite Fields of Small Characteristic

A Heuristic Quasi-Polynomial Algorithm for Discrete Logarithm in Finite Fields of Small Characteristic

Redefinition of Words: Racism An article about the redefinition and abuse of the word Racism.

Redefinition of Words: Racism An article about the redefinition and abuse of the word Racism.

Algebra 2 students get to mix and match function cards (absolute value, radical and quadratic) with characteristic cards (range interval, increasing interval or decreasing interval) and then either graph or write the equation of the mix-match (based on the card's directions). There are 162 combinations! Each student in the group should complete each mix-match so that they can check each other.

Students love choice in Algebra 2

Algebra 2 students get to mix and match function cards (absolute value, radical and quadratic) with characteristic cards (range interval, increasing interval or decreasing interval) and then either graph or write the equation of the mix-match (based on the card's directions). There are 162 combinations! Each student in the group should complete each mix-match so that they can check each other.

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