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Polynomial expressions, equations, & functions

Intro to polynomials

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Polynomials intro
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The parts of polynomial expressions
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Evaluating polynomials
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Simplifying polynomials
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Practice
Polynomials intro
4 questions

Adding & subtracting polynomials

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Adding polynomials
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Subtracting polynomials
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Polynomial subtraction & set closure
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Adding & subtracting multiple polynomials
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Adding polynomials (old)
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Adding and subtracting polynomials review
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Practice
Add polynomials (intro)
4 questions
Subtract polynomials (intro)
4 questions
Add & subtract polynomials
4 questions

Adding & subtracting polynomials: two variables

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Adding polynomials: two variables
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Subtracting polynomials: two variables
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Subtracting polynomials: two variables
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Finding an error in polynomial subtraction
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Polynomials review
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Adding and subtracting polynomials with two variables review
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Practice
Add & subtract polynomials: two variables (intro)
4 questions
Add & subtract polynomials: two variables
4 questions
Add & subtract polynomials: find the error
4 questions

Multiplying monomials

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Multiplying monomials
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Multiplying monomials to find area: two variables
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Multiplying monomials to find area
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Multiplying monomials challenge
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Multiplying monomials review
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Practice
Multiply monomials intro
4 questions
Multiply monomials
4 questions

Multiplying monomials by polynomials

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Multiplying monomials by polynomials: area model
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Multiplying monomials by polynomials
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Multiplying monomials by polynomials challenge
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Multiplying monomials by polynomials review
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Practice
Multiply monomials by polynomials: area model
4 questions
Multiply monomials by polynomials
4 questions
Multiply monomials by polynomials challenge
4 questions

Multiplying binomials

Learn
Multiplying binomials: area model
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Multiplying binomials intro
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Multiplying binomials
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Multiplying binomials review
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Practice
Multiply binomials: area model
4 questions
Warmup: multiplying binomials intro
4 questions
Multiply binomials intro
4 questions
Multiply binomials
4 questions

Special products of binomials

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Special products of the form (x+a)(x-a)
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Squaring binomials of the form (x+a)²
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Special products of the form (ax+b)(ax-b)
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Squaring binomials of the form (ax+b)²
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Special products of binomials: two variables
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More examples of special products
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Squaring a binomial (old)
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Binomial special products review
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Practice
Special products of binomials intro
4 questions
Special products of binomials
4 questions

Multiplying binomials by polynomials

Learn
Multiplying binomials by polynomials
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Multiplying binomials by polynomials: area model
(Opens a modal)
Multiplying binomials by polynomials challenge
(Opens a modal)
Multiplying binomials by polynomials review
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Multiplying binomials by polynomials (old)
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Multiplying binomials with radicals (old)
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Practice
Multiply binomials by polynomials
4 questions

Polynomials word problems

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Polynomial multiplication word problem
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Polynomial word problem: rectangle and circle area
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Polynomial word problem: total value of bills
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Polynomial word problem: area of a window
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Introduction to factorization

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Intro to factors & divisibility
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Intro to factors & divisibility
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Practice
Factors & divisibility
4 questions

Factoring monomials

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Monomial factorization
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Factoring monomials
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Worked example: finding the missing monomial factor
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Worked example: finding missing monomial side in area model
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Greatest common factor of monomials
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Greatest common factor of monomials
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Practice
Factor monomials
4 questions
Greatest common factor of monomials
4 questions

Factoring polynomials by taking common factors

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Factoring with the distributive property
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Factoring polynomials by taking a common factor
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Factoring binomials: common factor
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Factoring polynomials: common factor
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Factoring polynomials: common factor area model
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Factoring polynomials: common binomial factor
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Factoring by common factor review
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Factoring polynomials: common factor (old)
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Factoring polynomials: common factor (old)
(Opens a modal)
Practice
Factor polynomials: common factor
4 questions

Evaluating expressions with unknown variables

Learn
Worked example: evaluating expressions using structure
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Worked example: evaluating expressions using structure (more examples)
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Practice
Evaluate expressions using structure
4 questions

Factoring quadratics intro

Learn
Factoring quadratics as (x+a)(x+b)
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Factoring quadratics: leading coefficient = 1
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Factoring quadratics as (x+a)(x+b) (example 2)
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More examples of factoring quadratics as (x+a)(x+b)
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Factoring simple quadratics review
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Practice
Warmup: factoring quadratics intro
4 questions
Factoring quadratics intro
4 questions

Factoring quadratics by grouping

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Intro to grouping
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Factoring by grouping
(Opens a modal)
Factoring quadratics by grouping
(Opens a modal)
Factoring quadratics: leading coefficient ≠ 1
(Opens a modal)
Practice
Factor quadratics by grouping
4 questions

Factoring polynomials with quadratic forms

Learn
Factoring quadratics: common factor + grouping
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Factoring quadratics: negative common factor + grouping
(Opens a modal)
Factoring two-variable quadratics
(Opens a modal)
Factoring two-variable quadratics: rearranging
(Opens a modal)
Factoring two-variable quadratics: grouping
(Opens a modal)
Factoring quadratics with common factor (old)
(Opens a modal)
Practice
Factor polynomials: quadratic methods
4 questions
Factor polynomials: quadratic methods (challenge)
4 questions

Factoring quadratics: Difference of squares

Learn
Difference of squares intro
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Factoring quadratics: Difference of squares
(Opens a modal)
Factoring difference of squares: leading coefficient ≠ 1
(Opens a modal)
Factoring difference of squares: analyzing factorization
(Opens a modal)
Factoring difference of squares: missing values
(Opens a modal)
Factoring difference of squares: shared factors
(Opens a modal)
Practice
Difference of squares intro
4 questions
Difference of squares
4 questions

Factoring quadratics: Perfect squares

Learn
Perfect square factorization intro
(Opens a modal)
Factoring quadratics: Perfect squares
(Opens a modal)
Factoring perfect squares
(Opens a modal)
Identifying perfect square form
(Opens a modal)
Factoring perfect squares: common factor
(Opens a modal)
Factoring perfect squares: negative common factor
(Opens a modal)
Factoring perfect squares: missing values
(Opens a modal)
Factoring perfect squares: shared factors
(Opens a modal)
Practice
Perfect squares intro
4 questions
Perfect squares
4 questions

Strategy in factoring quadratics

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

Factoring polynomials with special product forms

Learn
Factoring perfect squares: 4th degree polynomial
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Factoring difference of squares: two variables
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Factoring difference of squares: two variables (example 2)
(Opens a modal)
Practice
Factor polynomials: special product forms
4 questions
Factoring polynomials challenge
6 questions

Long division of polynomials

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Intro to long division of polynomials
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Dividing polynomials: long division
(Opens a modal)

Synthetic division of polynomials

Learn
Intro to polynomial synthetic division
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Dividing polynomials: synthetic division
(Opens a modal)
Why synthetic division works
(Opens a modal)

Practice dividing polynomials with remainders

Learn
Dividing polynomials with remainders: monomial divisors
(Opens a modal)
Dividing polynomials with remainders: monomial divisors (example 2)
(Opens a modal)
Dividing polynomials with remainders
(Opens a modal)
Practice
Divide polynomials with remainders: monomial divisors
4 questions
Divide polynomials with remainders: binomial divisors
4 questions
Divide polynomials with remainders
4 questions

Polynomial Remainder Theorem

Learn
Intro to the Polynomial Remainder Theorem
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Using the Polynomial Remainder Theorem: finding remainders
(Opens a modal)
Using the Polynomial Remainder Theorem: checking factors
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Using the Polynomial Remainder Theorem: finding coefficients
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Proof of the Polynomial Remainder Theorem
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Practice
Use the Polynomial Remainder Theorem
4 questions

Binomial theorem

Learn
Intro to the Binomial Theorem
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Pascal's triangle and binomial expansion
(Opens a modal)
Expanding binomials
(Opens a modal)
Expanding binomials w/o Pascal's triangle
(Opens a modal)
Practice
Expand binomials
4 questions

Understanding the binomial theorem

Learn
Binomial expansion & combinatorics
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Pascal's triangle & combinatorics
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Binomial expansion & combinatorics (old)
(Opens a modal)

Advanced polynomial factorization methods

Learn
Factoring higher-degree polynomials
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Factoring sum of cubes
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Factoring difference of cubes
(Opens a modal)

Proving polynomial identities

Learn
Analyzing polynomial identities
(Opens a modal)
Practice
Prove polynomial identities
4 questions

Polynomial identities with complex numbers

Learn
Complex numbers & sum of squares factorization
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Factoring sum of squares
(Opens a modal)
Practice
Factor polynomials: complex numbers
4 questions

Quadratic equations with complex numbers

Learn
Solving quadratic equations: complex roots
(Opens a modal)
Practice
Solve quadratic equations: complex solutions
4 questions

Fundamental Theorem of Algebra

Learn
The Fundamental theorem of Algebra
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Quadratics & the Fundamental Theorem of Algebra
(Opens a modal)
Number of possible real roots of a polynomial
(Opens a modal)

Finding zeros of polynomials

Learn
Finding zeros of polynomials (1 of 2)
(Opens a modal)
Finding zeros of polynomials (2 of 2)
(Opens a modal)
Finding zeros of polynomials (example 2)
(Opens a modal)
Practice
Finding zeros of polynomials
4 questions
Zeros of polynomials challenge problems
5 questions

Zeros of polynomials and their graphs

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Zeros of polynomials & their graphs
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Zeros of polynomials & their graphs
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Positive & negative intervals of polynomials
(Opens a modal)
Practice
Zeros of polynomials & their graphs
4 questions
Positive & negative intervals of polynomials
4 questions

End behavior of polynomial functions

Learn
Intro to end behavior of polynomials
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End behavior of polynomials
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End behavior of functions & their graphs
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Practice
End behavior of polynomials
4 questions

Graphs of polynomials

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Graphs of polynomials
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Graphs of polynomials: Challenge problems
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Introduction to symmetry of functions

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Intro to function symmetry
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Intro to symmetry of functions
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Graphical symmetry of functions
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Even/odd functions & numbers
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Practice
Even & odd functions
4 questions

Symmetry of polynomial functions

Learn
Even & odd polynomials
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Symmetry of polynomials
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Practice
Even & odd polynomials
4 questions

Unit test

Test your understanding of Polynomial expressions, equations, & functions with these 48 questions.

About this unit

This topic covers: - Adding, subtracting, and multiplying polynomial expressions - Factoring polynomial expressions as the product of linear factors - Dividing polynomial expressions - Proving polynomials identities - Solving polynomial equations & finding the zeros of polynomial functions - Graphing polynomial functions - Symmetry of functions