# Polynomial expressions, equations, & functions

## Intro to polynomials

Learn
Polynomials introThe parts of polynomial expressionsEvaluating polynomialsSimplifying polynomials
Practice

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## Adding & subtracting polynomials: two variables

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Adding polynomials: two variables (intro)Subtracting polynomials: two variables (intro)Subtracting polynomials: two variablesFinding an error in polynomial subtractionPolynomials reviewAdding and subtracting polynomials with two variables review

## Multiplying monomials

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Multiplying monomialsMultiplying monomials to find area: two variablesMultiplying monomials to find areaMultiplying monomials challengeMultiplying monomials review
Practice

## Multiplying monomials by polynomials

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Multiplying monomials by polynomials: area modelMultiplying monomials by polynomialsMultiplying monomials by polynomials challengeMultiplying monomials by polynomials review

## Multiplying binomials

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Multiplying binomials: area modelMultiplying binomials introMultiplying binomialsMultiplying binomials review

## Special products of binomials

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Special products of the form (x+a)(x-a)Squaring binomials of the form (x+a)²Special products of the form (ax+b)(ax-b)Squaring binomials of the form (ax+b)²Special products of binomials: two variablesMore examples of special productsSquaring a binomial (old)Binomial special products review

## Multiplying binomials by polynomials

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Multiplying binomials by polynomialsMultiplying binomials by polynomials: area modelMultiplying binomials by polynomials challengeMultiplying binomials by polynomials reviewMultiplying binomials by polynomials (old)Multiplying binomials with radicals (old)

## Polynomials word problems

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Polynomial multiplication word problemPolynomial word problem: rectangle and circle areaPolynomial word problem: total value of billsPolynomial word problem: area of a window

## Introduction to factorization

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Intro to factors & divisibilityIntro to factors & divisibility
Practice

## Factoring monomials

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Which monomial factorization is correct?Factoring monomialsWorked example: finding the missing monomial factorWorked example: finding missing monomial side in area modelGreatest common factor of monomialsGreatest common factor of monomials

## Factoring polynomials by taking common factors

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Factoring with the distributive propertyFactoring polynomials by taking a common factorTaking common factor from binomialTaking common factor from trinomialTaking common factor: area modelFactoring polynomials: common binomial factorFactoring by common factor reviewFactoring polynomials: common factor (old)Factoring polynomials: common factor (old)

## Evaluating expressions with unknown variables

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Worked example: evaluating expressions using structureWorked example: evaluating expressions using structure (more examples)

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Learn

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## Factoring quadratics: Difference of squares

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Difference of squares introFactoring quadratics: Difference of squaresFactoring difference of squares: leading coefficient ≠ 1Factoring difference of squares: analyzing factorizationFactoring difference of squares: missing valuesFactoring difference of squares: shared factors

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Perfect square factorization introFactoring quadratics: Perfect squaresFactoring perfect squaresIdentifying perfect square formFactoring higher-degree polynomials: Common factorFactoring perfect squares: negative common factorFactoring perfect squares: missing valuesFactoring perfect squares: shared factors
Practice
4 questions

Learn
Strategy in factoring quadratics (part 1 of 2)Strategy in factoring quadratics (part 2 of 2)Factoring quadratics in any form

## Factoring polynomials with special product forms

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Factoring using the perfect square patternFactoring using the difference of squares patternFactoring difference of squares: two variables (example 2)

## Long division of polynomials

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Intro to long division of polynomialsDividing polynomials: long division

## Synthetic division of polynomials

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Intro to polynomial synthetic divisionDividing polynomials: synthetic divisionWhy synthetic division works

## Practice dividing polynomials with remainders

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Divide polynomials by x (with remainders)Divide polynomials by monomials (with remainders)Dividing polynomials with remainders

## Polynomial Remainder Theorem

Learn
Intro to the Polynomial Remainder TheoremRemainder theorem: finding remainder from equationRemainder theorem: checking factorsRemainder theorem: finding coefficientsProof of the Polynomial Remainder Theorem
Practice

## Binomial theorem

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Intro to the Binomial TheoremPascal's triangle and binomial expansionExpanding binomialsExpanding binomials w/o Pascal's triangle
Practice
4 questions

## Understanding the binomial theorem

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Binomial expansion & combinatoricsPascal's triangle & combinatoricsBinomial expansion & combinatorics (old)

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Factoring higher-degree polynomialsFactoring sum of cubesFactoring difference of cubes

## Proving polynomial identities

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Analyzing polynomial identities
Practice

## Polynomial identities with complex numbers

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Complex numbers & sum of squares factorizationFactoring sum of squares

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## Fundamental Theorem of Algebra

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The Fundamental theorem of AlgebraQuadratics & the Fundamental Theorem of Algebra Number of possible real roots of a polynomial

## Finding zeros of polynomials

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Finding zeros of polynomials (1 of 2)Finding zeros of polynomials (2 of 2)Finding zeros of polynomials (example 2)

## Zeros of polynomials and their graphs

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Zeros of polynomials & their graphsZeros of polynomials & their graphsPositive & negative intervals of polynomials

## End behavior of polynomial functions

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Intro to end behavior of polynomialsEnd behavior of polynomialsEnd behavior of functions & their graphs
Practice

## Graphs of polynomials

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Graphs of polynomialsGraphs of polynomials: Challenge problems

## Introduction to symmetry of functions

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Function symmetry introductionFunction symmetry introductionEven and odd functions: GraphsEven/odd functions & numbers

## Symmetry of polynomial functions

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Even & odd polynomialsSymmetry of polynomials

#### Unit test

Test your understanding of Polynomial expressions, equations, & functions with these 46 questions.