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Module 1: Polynomial, rational, and radical relationships

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Lessons 1-2: No content yetIntro to long division of polynomialsDividing polynomials: long divisionDivide polynomials by x (with remainders)Divide polynomials by monomials (with remainders)Dividing polynomials with remaindersLessons 7-11: No content yet
Practice
Divide polynomials by linear expressionsGet 3 of 4 questions to level up!
Divide polynomials with remaindersGet 3 of 4 questions to level up!
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Factoring quadratics: common factor + groupingFactoring quadratics: negative common factor + groupingFactoring two-variable quadraticsFactoring two-variable quadratics: rearrangingFactoring two-variable quadratics: groupingFactoring using the perfect square patternFactoring using the difference of squares patternFactoring difference of squares: two variables (example 2)Factoring higher-degree polynomialsFactoring sum of cubesFactoring difference of cubesFinding zeros of polynomials (1 of 2)Finding zeros of polynomials (2 of 2)Finding zeros of polynomials (example 2)
Practice
Factor polynomials: quadratic methodsGet 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!
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Zeros of polynomials & their graphsZeros of polynomials & their graphsPositive & negative intervals of polynomialsIntro to end behavior of polynomialsEnd behavior of polynomialsEnd behavior of functions & their graphsGraphs of polynomialsGraphs of polynomials: Challenge problems
Practice
Zeros of polynomials (factored form)Get 3 of 4 questions to level up!
End behavior of polynomialsGet 3 of 4 questions to level up!
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Function symmetry introductionFunction symmetry introductionEven and odd functions: GraphsEven/odd functions & numbersEven & odd polynomialsSymmetry of polynomials
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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Lessons 16-17: No content yetIntro to the Polynomial Remainder TheoremRemainder theorem: finding remainder from equationRemainder theorem: checking factorsRemainder theorem: finding coefficientsProof of the Polynomial Remainder TheoremLessons 20-21: No content yet
Practice
Remainder theoremGet 3 of 4 questions to level up!
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Intro to rational expression simplificationIntro to rational expressionsIntro to simplifying rational expressionsSimplifying rational expressions: common monomial factorsSimplifying rational expressions: common binomial factorsSimplifying rational expressions: opposite common binomial factorsSimplifying rational expressions (advanced)Simplifying rational expressions: groupingSimplifying rational expressions: higher degree termsSimplifying rational expressions: two variablesLesson 23: No content yet
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Multiplying & dividing rational expressions: monomialsMultiplying rational expressionsDividing rational expressionsMultiplying rational expressionsDividing rational expressionsMultiplying rational expressions: multiple variablesDividing rational expressions: unknown expression
Practice
Multiply & divide rational expressionsGet 3 of 4 questions to level up!
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Adding & subtracting rational expressions: like denominatorsIntro to adding & subtracting rational expressionsIntro to adding rational expressions with unlike denominatorsAdding rational expression: unlike denominatorsSubtracting rational expressions: unlike denominatorsLeast common multipleLeast common multiple: repeating factorsSubtracting rational expressions: factored denominatorsLeast common multiple of polynomialsAdding & subtracting rational expressions (advanced)Subtracting rational expressionsNested fractions
Practice
Least common multipleGet 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!
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Rational equations introEquations with one rational expression (advanced)Equations with rational expressionsEquations with rational expressions (example 2)Rational equations word problem: combined ratesRational equations word problem: combined rates (example 2)Rational equations word problem: eliminating solutions
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!
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Intro to square-root equations & extraneous solutionsIntro to solving square-root equationsSolving square-root equationsSolving square-root equations: one solutionSolving square-root equations: two solutionsSolving square-root equations: no solutionSquare-root equations introEquation that has a specific extraneous solutionExtraneous solutions of radical equationsSolving cube-root equations
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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Intro to linear systems with 3 variablesSolving linear systems with 3 variablesSolving linear systems with 3 variables: no solution3-variable linear system word problem
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Quadratic systems: graphical solutionQuadratic system with no solutionsQuadratic systems: both variables are squaredQuadratic systems: a line and a circle
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Interpreting equations graphicallyInterpreting equations graphically (example 2)Solving equations graphically (1 of 2)Solving equations graphically (2 of 2)Solving equations graphically
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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Intro to focus & directrixEquation of a parabola from focus & directrixFocus & directrix of a parabola from equation Parabola focus & directrix review
Practice
Learn
Intro to the imaginary numbersIntro to the imaginary numbersSimplifying roots of negative numbersi as the principal root of -1Intro to complex numbersPlotting numbers on the complex planeThe complex plane
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
Adding complex numbersSubtracting complex numbersMultiplying complex numbersMultiplying complex numbersPowers of the imaginary unitPowers of the imaginary unit
Practice
Add & subtract complex numbersGet 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
Solving quadratic equations: complex rootsComplex numbers & sum of squares factorizationFactoring sum of squaresThe Fundamental theorem of AlgebraQuadratics & the Fundamental Theorem of Algebra Number of possible real roots of a polynomial
Practice
Factor polynomials: complex numbersGet 3 of 4 questions to level up!

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