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- HSA-APR.D.6Rewrite simple rational expressions in different forms; write <sup>a(x)</sup>/<sub>b(x)</sub> in the form q(x) + <sup>r(x)</sup>/<sub>b(x)</sub>, where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.
- HSA-APR.D.7(+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.

HSA-APR.D.6

Rewrite simple rational expressions in different forms; write ^{a(x)}/_{b(x)} in the form q(x) + ^{r(x)}/_{b(x)}, where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.

Speed Dating Rationally

12th Grade Math

» Unit:

Rational Functions and Equations

Big Idea:Efficiency and accuracy improves as students solve rational equations with their ‘date’ in this interactive and self-checking speed dating activity.

Proving Polynomial Identities

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.

Review of Polynomial Roots and Complex Numbers

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.

The Remainder Theorem

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).

Rationally Synthetic

Algebra II

» Unit:

Algebraic Arithmetic

Big Idea:Help your students connect the dots from long division to polynomial long division to synthetic division.

Quiz and Intro to Graphs of Polynomials

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.

Seeing Structure in Expressions - Factoring Higher Order Polynomials

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.

Polynomial Long Division and Solving Polynomial Equations

Algebra II

» Unit:

Polynomial Theorems and Graphs

Big Idea:Operations with polynomials are a lot like operations with integers.

Polynomial Long Division

Algebra II

» Unit:

Higher-Degree Polynomials

Big Idea:Mastery of polynomial long division comes with practice and reflection on the nature of the algorithm.

The Fundamental Theorem of Algebra and Imaginary Solutions

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.

The Remainder Theorem, Day 1 of 2

Algebra II

» Unit:

Higher-Degree Polynomials

Big Idea:Students make sense of the many connections between polynomial factors, zeros, and remainders from polynomial long division.

Polynomial Long Division

Algebra II

» Unit:

Polynomial Functions

Big Idea:Connect students to the math they did in fifth grade with this lesson on polynomial long division.

Arithmetic with Complex Numbers

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.

Synthetic Division

Algebra II

» Unit:

Polynomial Functions

Big Idea:Connect students to the math they did in fifth grade with this lesson on polynomial long division.

Performance Task - Representing Polynomials

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.

HSA-APR.D.6

Rewrite simple rational expressions in different forms; write ^{a(x)}/_{b(x)} in the form q(x) + ^{r(x)}/_{b(x)}, where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.

HSA-APR.D.7

(+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.