Polynomial expressions, equations, & functions

Intro to polynomials

Learn

Polynomials intro
(Opens a modal)
The parts of polynomial expressions
(Opens a modal)
Evaluating polynomials
(Opens a modal)
Simplifying polynomials
(Opens a modal)

Practice

Polynomials intro
4 questions

Adding & subtracting polynomials

Learn

Adding polynomials
(Opens a modal)
Subtracting polynomials
(Opens a modal)
Polynomial subtraction & set closure
(Opens a modal)
Adding & subtracting multiple polynomials
(Opens a modal)
Adding polynomials (old)
(Opens a modal)
Adding and subtracting polynomials review
(Opens a modal)

Practice

Add polynomials (intro)
4 questions
Subtract polynomials (intro)
4 questions
Add & subtract polynomials
4 questions

Adding & subtracting polynomials: two variables

Learn

Adding polynomials: two variables
(Opens a modal)
Subtracting polynomials: two variables
(Opens a modal)
Subtracting polynomials: two variables challenge
(Opens a modal)
Finding an error in polynomial subtraction
(Opens a modal)
Polynomials review
(Opens a modal)
Adding and subtracting polynomials with two variables review
(Opens a modal)

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

Learn

Multiplying monomials
(Opens a modal)
Multiplying monomials to find area: two variables
(Opens a modal)
Multiplying monomials to find area
(Opens a modal)
Multiplying monomials challenge
(Opens a modal)
Multiplying monomials review
(Opens a modal)

Practice

Multiply monomials intro
4 questions
Multiply monomials
4 questions

Multiplying monomials by polynomials

Learn

Multiplying monomials by polynomials: area model
(Opens a modal)
Multiplying monomials by polynomials
(Opens a modal)
Multiplying monomials by polynomials challenge
(Opens a modal)
Multiplying monomials by polynomials review
(Opens a modal)

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
(Opens a modal)
Multiplying binomials intro
(Opens a modal)
Multiplying binomials
(Opens a modal)
Multiplying binomials review
(Opens a modal)

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

Learn

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

Practice

Special products of binomials intro
4 questions
Special products of binomials
4 questions

Multiplying binomials by polynomials

Learn

Multiplying binomials by polynomials
(Opens a modal)
Multiplying binomials by polynomials: area model
(Opens a modal)
Multiplying binomials by polynomials challenge
(Opens a modal)
Multiplying binomials by polynomials review
(Opens a modal)
Multiplying binomials by polynomials (old)
(Opens a modal)
Multiplying binomials with radicals (old)
(Opens a modal)

Practice

Multiply binomials by polynomials
4 questions

Polynomials word problems

Learn

Polynomial multiplication word problem
(Opens a modal)
Polynomial word problem: rectangle and circle area
(Opens a modal)
Polynomial word problem: total value of bills
(Opens a modal)
Polynomial word problem: area of a window
(Opens a modal)

Introduction to factorization

Learn

Intro to factors & divisibility
(Opens a modal)
Intro to factors & divisibility
(Opens a modal)

Practice

Factors & divisibility
4 questions

Factoring monomials

Learn

Monomial factorization
(Opens a modal)
Factoring monomials
(Opens a modal)
Worked example: finding the missing monomial factor
(Opens a modal)
Worked example: finding missing monomial side in area model
(Opens a modal)
Greatest common factor of monomials
(Opens a modal)
Greatest common factor of monomials
(Opens a modal)

Practice

Factor monomials
4 questions
Greatest common factor of monomials
4 questions

Factoring polynomials by taking common factors

Learn

Factoring with the distributive property
(Opens a modal)
Factoring polynomials by taking a common factor
(Opens a modal)
Factoring binomials: common factor
(Opens a modal)
Factoring polynomials: common factor
(Opens a modal)
Factoring polynomials: common factor area model
(Opens a modal)
Factoring polynomials: common binomial factor
(Opens a modal)
Factoring by common factor review
(Opens a modal)
Factoring polynomials: common factor (old)
(Opens a modal)
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
(Opens a modal)
Worked example: evaluating expressions using structure (more examples)
(Opens a modal)

Practice

Evaluate expressions using structure
4 questions

Factoring quadratics intro

Learn

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

Practice

Warmup: factoring quadratics intro
4 questions
Factoring quadratics intro
4 questions

Factoring quadratics by grouping

Learn

Intro to grouping
(Opens a modal)
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
(Opens a modal)
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
(Opens a modal)
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

Learn

Strategy in factoring quadratics (part 1 of 2)
(Opens a modal)
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
(Opens a modal)
Factoring difference of squares: two variables
(Opens a modal)
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

Learn

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

Synthetic division of polynomials

Learn

Intro to polynomial synthetic division
(Opens a modal)
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
(Opens a modal)
Using the Polynomial Remainder Theorem: finding remainders
(Opens a modal)
Using the Polynomial Remainder Theorem: checking factors
(Opens a modal)
Using the Polynomial Remainder Theorem: finding coefficients
(Opens a modal)
Proof of the Polynomial Remainder Theorem
(Opens a modal)

Practice

Use the Polynomial Remainder Theorem
4 questions

Binomial theorem

Learn

Intro to the Binomial Theorem
(Opens a modal)
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
(Opens a modal)
Pascal's triangle & combinatorics
(Opens a modal)
Binomial expansion & combinatorics (old)
(Opens a modal)

Advanced polynomial factorization methods

Learn

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

Find zeros of polynomials
4 questions
Zeros of polynomials challenge problems
5 questions

Zeros of polynomials and their graphs

Learn

Zeros of polynomials & their graphs
(Opens a modal)
Zeros of polynomials & their graphs
(Opens a modal)
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
(Opens a modal)
End behavior of polynomials
(Opens a modal)
End behavior of functions & their graphs
(Opens a modal)

Practice

End behavior of polynomials
4 questions

Graphs of polynomials

Learn

Graphs of polynomials
(Opens a modal)
Graphs of polynomials: Challenge problems
(Opens a modal)

Introduction to symmetry of functions

Learn

Intro to function symmetry
(Opens a modal)
Intro to symmetry of functions
(Opens a modal)
Graphical symmetry of functions
(Opens a modal)
Even/odd functions & numbers
(Opens a modal)

Practice

Even & odd functions
4 questions

Symmetry of polynomial functions

Learn

Even & odd polynomials
(Opens a modal)
Symmetry of polynomials
(Opens a modal)

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