Key Concepts:
- Factors of an expression are numbers or expressions that divide the original expression completely.
- An algebraic expression can be written as a product of all its factors.
- Quadratic Expressions can be simplified using common factorization techniques such as Difference of Squares, Perfect Square Trinomials, and Grouping.
- Difference of Squares: (a^2 - b^2 = (a - b)(a + b)).
- Factoring Perfect Square Trinomials: (a^2 + 2ab + b^2 = (a + b)^2).
Skills Covered:
- Factoring binomials and trinomials into simpler expressions.
- Identifying expressions that follow special factoring rules.
- Applying formulas to simplify polynomial expressions.
Example Problems:
- Factor: (6x^2 + 9x); Solution: (3x(2x + 3))
- Factor: (2x^2 + 8x + 6); Solution: (2(x^2 + 4x + 3) = 2(x+3)(x+1))
- Factor: (9y^2 - 25); Solution: ((3y - 5)(3y + 5))