# Unit 1: Module 1: Polynomial, rational, and radical relationships

## About this unit

"Students connect polynomial arithmetic to computations with whole numbers and integers. Students learn that the arithmetic of rational expressions is governed by the same rules as the arithmetic of rational numbers. This unit helps students see connections between solutions to polynomial equations, zeros of polynomials, and graphs of polynomial functions. Polynomial equations are solved over the set of complex numbers, leading to a beginning understanding of the fundamental theorem of algebra. Application and modeling problems connect multiple representations and include both real world and purely mathematical situations." Eureka Math/EngageNY (c) 2015 GreatMinds.org

### Learn

### Practice

- Multiply binomials by polynomials: area modelGet 3 of 4 questions to level up!
- Multiply binomials by polynomialsGet 3 of 4 questions to level up!
- Divide polynomials by monomials (with remainders) Get 3 of 4 questions to level up!
- Divide polynomials by linear expressionsGet 3 of 4 questions to level up!
- Divide polynomials with remaindersGet 3 of 4 questions to level up!
- Simplify square rootsGet 3 of 4 questions to level up!
- Simplify square roots (variables)Get 3 of 4 questions to level up!

### Learn

### Practice

- Factor polynomials: quadratic methodsGet 3 of 4 questions to level up!
- Factor polynomials: quadratic methods (challenge)Get 3 of 4 questions to level up!
- Factor polynomials using structureGet 3 of 4 questions to level up!
- Zeros of polynomials (with factoring)Get 3 of 4 questions to level up!

### Learn

### Practice

- Zeros of polynomials (factored form)Get 3 of 4 questions to level up!
- Positive & negative intervals of polynomialsGet 3 of 4 questions to level up!
- End behavior of polynomialsGet 3 of 4 questions to level up!

### Learn

### Practice

- Even and odd functions: Graphs and tablesGet 3 of 4 questions to level up!
- Even & odd functions: EquationsGet 3 of 4 questions to level up!

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### Practice

- Remainder theoremGet 3 of 4 questions to level up!

### Learn

### Practice

- Reduce rational expressions to lowest terms: Error analysisGet 3 of 4 questions to level up!
- Reduce rational expressions to lowest termsGet 3 of 4 questions to level up!
- Simplify rational expressions (advanced)Get 3 of 4 questions to level up!

### Learn

### Practice

- Multiply & divide rational expressions: Error analysisGet 3 of 4 questions to level up!
- Multiply & divide rational expressionsGet 3 of 4 questions to level up!
- Multiply & divide rational expressions (advanced)Get 3 of 4 questions to level up!

### Learn

### Practice

- Add & subtract rational expressions: like denominatorsGet 3 of 4 questions to level up!
- Add & subtract rational expressions (basic)Get 3 of 4 questions to level up!
- Least common multipleGet 3 of 4 questions to level up!
- Add & subtract rational expressions: factored denominatorsGet 3 of 4 questions to level up!
- Add & subtract rational expressionsGet 3 of 4 questions to level up!
- Nested fractionsGet 3 of 4 questions to level up!

### Learn

### Practice

- Rational equations introGet 3 of 4 questions to level up!
- Rational equations (advanced)Get 3 of 4 questions to level up!
- Rational equationsGet 3 of 4 questions to level up!
- Mixtures and combined rates word problemsGet 3 of 4 questions to level up!

### Learn

### Practice

- Square-root equations introGet 3 of 4 questions to level up!
- Square-root equationsGet 3 of 4 questions to level up!
- Extraneous solutions of equationsGet 3 of 4 questions to level up!

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### Practice

- Interpret equations graphically Get 3 of 4 questions to level up!
- Solve equations graphicallyGet 3 of 4 questions to level up!

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### Practice

- Equation of a parabola from focus & directrixGet 3 of 4 questions to level up!

### Learn

### Practice

- Simplify roots of negative numbersGet 3 of 4 questions to level up!
- Parts of complex numbersGet 3 of 4 questions to level up!
- Classify complex numbersGet 3 of 4 questions to level up!
- Plot numbers on the complex planeGet 3 of 4 questions to level up!

### Learn

### Practice

- Add & subtract complex numbersGet 3 of 4 questions to level up!
- Graphically add & subtract complex numbers Get 3 of 4 questions to level up!
- Multiply complex numbers (basic)Get 3 of 4 questions to level up!
- Multiply complex numbersGet 3 of 4 questions to level up!
- Powers of the imaginary unitGet 3 of 4 questions to level up!

### Learn

### Practice

- Solve quadratic equations: complex solutionsGet 3 of 4 questions to level up!
- Factor polynomials: complex numbersGet 3 of 4 questions to level up!