Main content

# Polynomial expressions, equations, & functions

Learn

Polynomials introThe parts of polynomial expressionsEvaluating polynomialsSimplifying polynomials

Practice

Learn

Adding polynomialsSubtracting polynomialsPolynomial subtractionAdding & subtracting multiple polynomialsAdding polynomials (old)Adding and subtracting polynomials review

Practice

Learn

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

Practice

Learn

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

Learn

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

Practice

Learn

Multiplying binomials: area modelMultiplying binomials introMultiplying binomialsMultiplying binomials review

Practice

Learn

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

Practice

Learn

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)

Practice

Learn

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

Learn

Intro to factors & divisibilityIntro to factors & divisibility

Practice

Learn

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

Learn

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)

Practice

Learn

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

Practice

Learn

Factoring quadratics as (x+a)(x+b)Factoring quadratics: leading coefficient = 1Factoring quadratics as (x+a)(x+b) (example 2)More examples of factoring quadratics as (x+a)(x+b)Factoring simple quadratics review

Learn

Intro to groupingFactoring by groupingFactoring quadratics by groupingFactoring quadratics: leading coefficient ≠ 1

Practice

Learn

Factoring quadratics: common factor + groupingFactoring quadratics: negative common factor + groupingFactoring two-variable quadraticsFactoring two-variable quadratics: rearrangingFactoring two-variable quadratics: groupingFactoring quadratics with common factor (old)

Practice

Learn

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

Learn

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

Learn

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

Learn

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

Practice

Learn

Intro to long division of polynomialsDividing polynomials: long division

Learn

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

Learn

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

Practice

Learn

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

Practice

Learn

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

Practice

Learn

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

Learn

Factoring higher-degree polynomialsFactoring sum of cubesFactoring difference of cubes

Learn

Analyzing polynomial identities

Practice

Learn

Complex numbers & sum of squares factorizationFactoring sum of squares

Practice

Learn

Solving quadratic equations: complex roots

Practice

Learn

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

Learn

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

Practice

Learn

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

Practice

Learn

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

Practice

Learn

Graphs of polynomialsGraphs of polynomials: Challenge problems

Learn

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

Practice

Learn

Even & odd polynomialsSymmetry of polynomials

Practice

Test your understanding of

**Polynomial expressions, equations, & functions**with these 46 questions.