Here, you can explore some advanced algebra lessons. These topics or lessons are usually covered in algebra 2 and include, among others, matrices, exponential and logarithmic functions, and some algebra proofs.

A more comprehensive list is shown below. Do not forget to check the section about 100 tough algebra word problems.

Prerequisites

- Polynomial functions
- How to write a polynomial from factored form to standard form
- How to write a polynomial from standard form to factored form
- How to write a polynomial function from its zeros
- How to find the zeros of a polynomial function
- Find the multiplicity of a zero
- Remainder theorem
- Rational root theorem
- Irrational root theorem
- Find rational roots using the rational root theorem
- Evaluate a polynomial by synthetic division
- Factor a higher-degree polynomial by using a quadratic pattern
- Solve a higher-degree polynomial by using a quadratic pattern

Examples of inductive reasoning

Proof by mathematical induction

Proof that square root of five is irrational

How to prove that there is no rational number whose square is 2

How to prove that the sum of a rational number and an irrational number is an irrational number

Proof of the Pythagorean theorem

A proof of the Pythagorean theorem by president Garfield is clearly explained here.

Proof of the quadratic formula

Here we prove the quadratic formula by completing the square

The different branches of algebra are beginning algebra, advanced algebra, linear algebra, abstract algebra, and commutative algebra.

The goal of these advanced algebra lessons is to help you become very familiar with high school algebra taught in 11th grade or sometimes in 12th grade. We will teach you most of the following topics:

- Graphing in three dimensions

- Learn to add, subtract, and multiply matrices

- Learn to graph quadratic equations

- Write and graph polynomials functions

- Solve polynomial equations

- Use important theorems about the number of solutions to polynomial equations

- Define, write, and evaluate exponential functions

- Define exponential growth and decay

- Modeling and graphing exponential growth and decay

- Define, write, and evaluate logarithms

- Simplify logarithms

- Expanding logarithms

- Properties of logarithms

- Solve exponential and logarithmic functions

- Learn how to prove things by induction

- Learn how to prove the Pythagorean theorem

- Learn how to prove the quadratic formula

- Learn to add, multiply, and graph complex numbers

- Use complex numbers to solve quadratic equations.