THE REMAINDER AND FACTOR THEOREM Chapter 5 5

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THE REMAINDER AND FACTOR THEOREM Chapter 5 -5 Algebra II

THE REMAINDER AND FACTOR THEOREM Chapter 5 -5 Algebra II

Focus Questions � Can you factor polynomials with long division? � What scenarios can

Focus Questions � Can you factor polynomials with long division? � What scenarios can this be utilized?

Curriculum standards HSA-APR. C. 4 - Prove polynomial identities and use them to describe

Curriculum standards HSA-APR. C. 4 - Prove polynomial identities and use them to describe numerical relationships. � TN 3103. 3. 23 (Associated Tennessee Learning Expectations) Understand the connection between the roots, zeros, xintercepts, factors of polynomials, and solutions of polynomial equations. � TN 3103. 3. 2 Associated Tennessee Learning Expectations) Students will be able to factor polynomials utilizing long division. � Sources: http: //www. corestandards. org/Math/Content/HSA/CED/A/1/ � Spring Board Algebra 2 Textbook �

Real World Examples Utilizing Factor and Remainder Theorem � What are examples of ways

Real World Examples Utilizing Factor and Remainder Theorem � What are examples of ways people utilize long division of polynomials in real world situations? ? ? ?

Real World Examples Utilizing Factor and Remainder Theorem - Manufacturing - Sports game attendance

Real World Examples Utilizing Factor and Remainder Theorem - Manufacturing - Sports game attendance

Academic language Polynomial long division: A method used to divide polynomials similar to the

Academic language Polynomial long division: A method used to divide polynomials similar to the way you divide numbers. This method is utilized when polynomials do not factor evenly. � Factor Theorem: A polynomial f(x) has a factor (x – k) if and only if f(k) = 0. We utilize this to find a zero of f. �

Polynomial Long Division

Polynomial Long Division

Polynomial Long Division

Polynomial Long Division

CHECK your answer!

CHECK your answer!

Polynomial Long Division

Polynomial Long Division

Polynomial Long Division

Polynomial Long Division

Remainder Theorem and Factor Theorem

Remainder Theorem and Factor Theorem

Polynomial Long Division Solving Zero of F

Polynomial Long Division Solving Zero of F

Practice Problem Solving Zero of F

Practice Problem Solving Zero of F

Real World Problem

Real World Problem

Real World Solution

Real World Solution

Practice Problems

Practice Problems

Review � How do we factor polynomials with long division? � What are the

Review � How do we factor polynomials with long division? � What are the real world scenarios this can be utilized in?

Review of terms �Explain the mathematical term: Polynomial Long Division. �Explain the Factor Theorem.

Review of terms �Explain the mathematical term: Polynomial Long Division. �Explain the Factor Theorem.

Practice + Homework Problems in a Group � 5. 5 Worksheet

Practice + Homework Problems in a Group � 5. 5 Worksheet

The Remainder and Factor Theorems The Remainder TheoremThe Remainder and Factor Theorems The Remainder Theorem
2 2 Remainder and Factor Theorems Remainder Theorem2 2 Remainder and Factor Theorems Remainder Theorem
REMAINDER THEOREM AND FACTOR THEOREM FUNCTIONAL NOTATION INPUTREMAINDER THEOREM AND FACTOR THEOREM FUNCTIONAL NOTATION INPUT
Long Division Remainder Theorem Factor Theorem Synthetic DivisionLong Division Remainder Theorem Factor Theorem Synthetic Division
The Factor and Remainder Theorems Revisited Remainder andThe Factor and Remainder Theorems Revisited Remainder and
Remainder Estimation Theorem Section 9 3 b RemainderRemainder Estimation Theorem Section 9 3 b Remainder
The Remainder and Factor Theorems Division The RemainderThe Remainder and Factor Theorems Division The Remainder
Polynomials The Remainder and Factor Theorems The remainderPolynomials The Remainder and Factor Theorems The remainder
Continuation of remainder factor theorem Introduction This ChapterContinuation of remainder factor theorem Introduction This Chapter
6 7 Remainder and Factor Theorem Warm Up6 7 Remainder and Factor Theorem Warm Up
2 5 Apply the Remainder and Factor Theorem2 5 Apply the Remainder and Factor Theorem
Factor Remainder Theorem Sketch the following curves statingFactor Remainder Theorem Sketch the following curves stating
Remainder Factor Theorem End Behavior Zeros Graphs PolynomialsRemainder Factor Theorem End Behavior Zeros Graphs Polynomials
SHAPE SPACE Pythagorean Theorem Pythagorean Theorem Pythagorean TheoremSHAPE SPACE Pythagorean Theorem Pythagorean Theorem Pythagorean Theorem
LEMIs Theorem Lamis Theorem Statement Lamis theorem isLEMIs Theorem Lamis Theorem Statement Lamis theorem is
VARIGNONS THEOREM What is Varigons Theorem The theoremVARIGNONS THEOREM What is Varigons Theorem The theorem
Thvenins Theorem Thevenins Theorem Thevenins theorem simplifies theThvenins Theorem Thevenins Theorem Thevenins theorem simplifies the
LEMIs Theorem Lamis Theorem Statement Lamis theorem isLEMIs Theorem Lamis Theorem Statement Lamis theorem is
Bayes Theorem Basics Total probability Theorem Bayes TheoremBayes Theorem Basics Total probability Theorem Bayes Theorem