Algebra Equations

Study Notes

Definition: An equation is a statement that says two mathematical expressions are equal.
Types of Equations:
- Linear Equations: Equations in which the highest power of the variable(s) is 1. (e.g., 2x + 3 = 5)
- Quadratic Equations: Equations in which the highest power of the variable(s) is 2. (e.g., x^2 + 4x + 4 = 0)
- Polynomial Equations: Equations involving polynomials.
Equation Operations:
- Addition and Subtraction: Adding or subtracting the same value to both sides of an equation.
- Multiplication and Division: Multiplying or dividing both sides of an equation by a non-zero value.

Definition: A polynomial is an expression consisting of variables and coefficients combined using only addition, subtraction, and multiplication.
Properties of Polynomials:
- Degree: The highest power of the variable(s) in a polynomial.
- Terms: Individual parts of a polynomial separated by addition or subtraction.
- Coefficients: Numbers multiplied by variables in a polynomial.
Operations with Polynomials:
- Addition and Subtraction: Combining like terms.
- Multiplication: Distributing each term of one polynomial to each term of the other polynomial.
Factoring Polynomials:
- Greatest Common Factor (GCF): Factoring out the largest common factor from each term.
- Difference of Squares: Factoring quadratic expressions in the form of a^2 - b^2 = (a + b)(a - b).

An equation is a statement that says two mathematical expressions are equal.
There are different types of equations, including:
- Linear Equations, where the highest power of the variable(s) is 1, e.g., 2x + 3 = 5.
- Quadratic Equations, where the highest power of the variable(s) is 2, e.g., x^2 + 4x + 4 = 0.
- Polynomial Equations, involving polynomials.
Equation operations include:
- Adding or subtracting the same value to both sides of an equation.
- Multiplying or dividing both sides of an equation by a non-zero value.

A polynomial is an expression consisting of variables and coefficients combined using only addition, subtraction, and multiplication.
Key properties of polynomials include:
- Degree, which is the highest power of the variable(s) in a polynomial.
- Terms, which are individual parts of a polynomial separated by addition or subtraction.
- Coefficients, which are numbers multiplied by variables in a polynomial.
Operations with polynomials include:
- Adding or subtracting polynomials by combining like terms.
- Multiplying polynomials by distributing each term of one polynomial to each term of the other polynomial.
Factoring polynomials involves:
- Finding the Greatest Common Factor (GCF) to factor out the largest common factor from each term.
- Using the Difference of Squares formula, a^2 - b^2 = (a + b)(a - b), to factor quadratic expressions.