Algebra 1 Factoring Flashcards

Factoring Techniques in Algebra 1

• Guess and Check Method: Used for factoring quadratics where the leading coefficient (a=1).

  • Example: x² - 3x - 18 factors to (x-6)(x+3).

• Difference of Squares: A technique for factoring expressions of the form (a² - b²).

  • Example: x² - 25 factors to (x - 5)(x + 5).
  • Example: 4x² - 81 factors to (2x - 9)(2x + 9).

• AC Method (Split and Group): Suitable for quadratics with a leading coefficient other than 1.

  • Factors using the product of (a) and (c) to split the middle term.
  • Example: 2x² - 3x - 5 factors to (2x - 5)(x + 1).

• Grouping Method: Involves grouping terms to factor common elements.

  • Example: ax - 3a + xy - 3y factors to (x - 3)(a + y).

• Greatest Common Factor (GCF): Identifying and factoring out the highest common factor.

  • Example: 12x³ - 9x² + 15x factors to 3x(4x² - 3x + 5).
  • Example: 30x² + 15x + 5 factors to 5(6x² + 3x + 1).

Important Factoring Examples

• Basic Quadratic Factoring:

  • x² + 5x + 6 factors to (x + 2)(x + 3).
  • x² - 7x + 12 factors to (x - 3)(x - 4).
  • x² + 6x - 16 factors to (x + 8)(x - 2).

• Factoring Special Forms:

  • x² - 1 factors to (x - 1)(x + 1).
  • x² - 36 factors to (x + 6)(x - 6).

• Multiple Terms:

  • 2x² + 9x + 10 factors to (2x + 5)(x + 2).
  • 5x² + 31x + 6 factors to (x + 6)(5x + 1).

• Higher Degree Factoring:

  • 9x⁴ - 16y² factors to (3x² - 4y)(3x² + 4y).

Review Tips

• Always look for the simplest factoring method first.
• Practice using each method with various polynomial forms to reinforce understanding.
• Break down complicated expressions by rearranging or adjacent grouping.
• Checking by expanding factors to confirm correctness prevents error.