Practice_dividing_polynomials_with_remainders
After learning about the different methods in which we can find the quotient and the remainder of two polynomials, gain some practice with actually performing polynomial division yourself.
Learn what factorization is all about, and warm-up by factoring some monomials.
Understanding_the_binomial_theorem
Now that you know how to use the binomial theorem in order to expand powers of binomial expressions, let's gain further insight into why this actually works!
As an intro to more elaborate polynomial multiplication, learn how to multiply monomials (which are polynomials with a single term). For example, multiply 2x³ and 5x⁷.
Learn how to factor quadratic expressions with a leading coefficient of 1. For example, factor x²+3x+2 as (x+1)(x+2).
Factoring_quadratics_Difference_of_squares
Learn how to factor quadratics that have the "difference of squares" form. For example, write x²-16 as (x+4)(x-4). Learn how to identify this form in more elaborate expressions. For example, write 4x²-49 as (2x+7)(2x-7).
Factoring_quadratics_Perfect_squares
Learn how to factor quadratics that have the "perfect square" form. For example, write x²+6x+9 as (x+3)². Learn how to identify these forms in more elaborate expressions. For example, write 4x²+28x+49 as (2x+7)².
Use all the knowledge you have about polynomials to find their zeros (which are the input values that make the polynomial equal to zero).
Combine your knowledge about the zeros and the end behavior of a polynomial in order to sketch its graph.
Fundamental_Theorem_of_Algebra
You may already have noticed that quadratic equations always have a solution when including complex number solutions. It turns out this is true for any polynomial equation, of any degree! Learn about this and more, right here.
Learn about common monomial factors and how to find the greatest common factor of two monomials. For example, find the greatest common factor of 6x^2y and 9xy^2 (answer: 3xy).
Learn how to multiply two binomials together. For example, (3x - 7) * (10x + 2).
Learn how to factor quadratic expressions with a leading coefficient other than 1. For example, factor 2x²+7x+3 as (2x+1)(x+3).
The polynomial remainder theorem allows us to easily determine whether a linear expression is a factor of a given polynomial. Learn exactly what the theorem means, practice using it, and learn about its proof.
Quadratic_equations_with_complex_numbers
Remember all these quadratic equations with "no real solution"? Well, it turns out those equations do have a solution, it's just a complex number! Solve a bunch of those here.
Learn about polynomial expressions: What are they? How are they constructed? What can we do with them?
Learn about the special types of products of binomials: perfect squares and the difference of two squares. These will be very helpful once you tackle more advanced expressions in Algebra.
Factoring_polynomials_by_taking_common_factors
Learn how to take a common monomial factor out of a polynomial expression. For example, write 2x^3+6x^2+8x as (2x)(x^2+3x+4).
Multiplying_monomials_by_polynomials
Learn how to multiply a polynomial expression by a monomial expression. Monomials are just polynomials with a single term!
End_behavior_of_polynomial_functions
Learn about the end behavior of polynomial functions. End behavior is the way the function behaves as the input values grow infinitely positive or infinitely negative.
Introduction_to_symmetry_of_functions
You may already be familiar with types of symmetries of geometrical shapes. Learn how functions can be symmetrical too!
Factoring_polynomials_with_quadratic_forms
Learn how to factor quadratic polynomials of the form ax^2+bx+c as the product of two linear binomials. For example, write x^2+3x-10 as (x+5)(x-2). Learn how to identify these forms in more elaborate polynomials that aren't necessarily quadratic. For example, write x^4-4x^2-12 as (x^2+2)(x^2-6).
Zeros_of_polynomials_and_their_graphs
Learn how to use the zeros of polynomials to draw a pretty good sketch of their graphs.
Practice proving polynomial identities, using all the factorization and expansion methods you know.
See a few examples of how we can represent real-world situations with polynomials.
Factoring_polynomials_with_special_product_forms
Factor polynomials of various degrees using factorization methods that are based on the special product forms "difference of squares" and "perfect squares." For example, factor 25x⁴-30x²+9 as (5x²-3)².
Synthetic_division_of_polynomials
Learn how to divide polynomials using long division.
Adding_subtracting_polynomials
Learn how to add and subtract polynomial expressions with one variable.
Advanced_polynomial_factorization_methods
Learn more ways to factor polynomials with degree higher than 2.
Adding_subtracting_polynomials_two_variables
Learn how to add and subtract polynomial that involve two variables. For example, x^3 + xy + 3y - (x^3 + 6xy + 2y^2).
Symmetry_of_polynomial_functions
Learn how to determine the symmetry of a polynomial function.
Learn how to write a monomial as a factor of two other monomials. For example, write 12x^3 as (4x)(3x^2).
Learn how to expand powers of binomial expressions (which are polynomial expressions with exactly two terms). This is done using the binomial theorem!
Polynomial_identities_with_complex_numbers
Prove more polynomial identities, this time including complex numbers!
Learn how to divide two polynomials using long division.
Multiplying_binomials_by_polynomials
Learn how to multiply a polynomial expression by a binomial expression.
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