Factoring Equations in Algebra 2

What is the purpose of factoring out the Greatest Common Factor (GCF) in an algebraic equation?

What is the general form of a quadratic equation that can be factored?

What is the formula for the difference of squares?

What is the purpose of checking your work by multiplying the factored form back out to the original equation?

What is the strategy for factoring quadratic equations?

What is the formula for the sum and difference?

Factoring Equations in Algebra 2

Factoring out the Greatest Common Factor (GCF)

Factor out the GCF from each term in the equation
Examples:
- 2x + 4 = 2(x + 2)
- 3x^2 + 6x = 3x(x + 2)

Factoring Quadratic Equations

General form: ax^2 + bx + c = (x + d)(x + e)
Factoring strategies:
- Look for two numbers whose product is ac and whose sum is b
- Examples:
  - x^2 + 5x + 6 = (x + 3)(x + 2)
  - x^2 - 7x + 12 = (x - 3)(x - 4)

Factoring Special Products

Difference of Squares: a^2 - b^2 = (a + b)(a - b)
- Examples:
  - x^2 - 4 = (x + 2)(x - 2)
  - x^2 - 9 = (x + 3)(x - 3)
Sum and Difference: a^2 + 2ab + b^2 = (a + b)^2, a^2 - 2ab + b^2 = (a - b)^2
- Examples:
  - x^2 + 6x + 9 = (x + 3)^2
  - x^2 - 4x + 4 = (x - 2)^2

Factoring by Grouping

Factor by grouping terms with common factors
Examples:
- x^2 + 3x + 2x + 6 = (x + 3)(x + 2)
- x^2 - 3x - 2x + 6 = (x - 3)(x - 2)

Tips and Strategies

Look for common factors among terms
Check for special products (difference of squares, sum and difference)
Factor out the GCF before trying other strategies
Check your work by multiplying the factored form back out to the original equation

Test your skills in factoring quadratic equations, including factoring out the Greatest Common Factor (GCF), factoring quadratic equations, special products, and factoring by grouping. Improve your algebra skills and learn tips and strategies for factoring equations.