Algebra Equations

Equations

• 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.

Polynomials

• 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).

Equations

• 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.

Polynomials

• 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.