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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 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!

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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: 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!

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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!

Positive & negative intervals of polynomialsGet 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

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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

Practice

Simplify rational expressions: common monomial factorsGet 3 of 4 questions to level up!

Simplify rational expressions: common binomial factorsGet 3 of 4 questions to level up!

Simplify rational expressions (advanced)Get 3 of 4 questions to level up!

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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 expressions (basic)Get 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!

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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

Add & subtract rational expressions: like denominatorsGet 3 of 4 questions to level up!

Add & subtract rational expressions: unlike denominatorsGet 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!

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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

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

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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!

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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!

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!

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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

Solve quadratic equations: complex solutionsGet 3 of 4 questions to level up!

Factor polynomials: complex numbersGet 3 of 4 questions to level up!