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Unit: Polynomials

0

Possible mastery points

The 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 binomialsGet 3 of 4 questions to level up!

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)

Factoring polynomials - Quadratic forms

Learn
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)
Intro to grouping
(Opens a modal)
Factoring quadratics by grouping
(Opens a modal)
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)
Practice
Factoring quadratics introGet 3 of 4 questions to level up!
Factor quadratics by groupingGet 3 of 4 questions to level up!
Factor polynomials: quadratic methodsGet 3 of 4 questions to level up!
Factor polynomials: quadratic methods (challenge)Get 3 of 4 questions to level up!

Factoring polynomials - Special product forms

Learn
Factoring using the difference of squares pattern
(Opens a modal)
Factoring difference of squares: leading coefficient ≠ 1
(Opens a modal)
Factoring perfect squares: negative common factor
(Opens a modal)
Factoring perfect squares
(Opens a modal)
Factoring using the perfect square pattern
(Opens a modal)
Factoring difference of squares: two variables (example 2)
(Opens a modal)
Practice
Difference of squares introGet 3 of 4 questions to level up!
Difference of squaresGet 3 of 4 questions to level up!
Perfect squaresGet 3 of 4 questions to level up!
Factor polynomials using structureGet 3 of 4 questions to level up!

Quiz 1

Level up on the above skills and collect up to 900 Mastery points

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
Polynomial identitiesGet 3 of 4 questions to level up!

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 numbersGet 3 of 4 questions to level up!

Quadratic equations with complex numbers

Learn
Solving quadratic equations: complex roots
(Opens a modal)
Practice
Solve quadratic equations: complex solutionsGet 3 of 4 questions to level up!

Quiz 2

Level up on the above skills and collect up to 300 Mastery points

The 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
Zeros of polynomials (with factoring)Get 3 of 4 questions to level up!

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 (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 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 polynomialsGet 3 of 4 questions to level up!

Graphs of polynomials

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

Quiz 3

Level up on the above skills and collect up to 400 Mastery points

Introduction to symmetry of functions

Learn
Function symmetry introduction
(Opens a modal)
Function symmetry introduction
(Opens a modal)
Even and odd functions: Graphs
(Opens a modal)
Even/odd functions & numbers
(Opens a modal)
Practice
Even and odd functions: Graphs and tablesGet 3 of 4 questions to level up!

Symmetry of polynomial functions

Learn
Even & odd polynomials
(Opens a modal)
Symmetry of polynomials
(Opens a modal)
Practice
Even & odd functions: EquationsGet 3 of 4 questions to level up!

Quiz 4

Level up on the above skills and collect up to 200 Mastery points
Up next for you:

Unit test

Level up on all the skills in this unit and collect up to 1800 Mastery points!

About this unit

Learn how to manipulate polynomials in order to prove identities and find the zeros of those polynomials. Use this knowledge to solve polynomial equations and graph polynomial functions. Learn about symmetry of functions.