Factoring Polynomials: Sum and Difference Formulas

Factoring Polynomials

Sum and Difference Formulas

• Sum of Cubes Formula: $a^3 + b^3 = (a + b)(a^2 - ab + b^2)$
• Difference of Cubes Formula: $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$

Factoring Out Greatest Common Factors (GCF)

• GCF: the largest number or expression that divides all terms of the polynomial
• Steps to factor out the GCF:
  1. Find the GCF of all terms
  2. Divide each term by the GCF
  3. Write the result as a product of the GCF and the remaining terms

Example: Factor $6x^2 + 12x + 18$ * GCF = 6 * Factor out 6: $6(x^2 + 2x + 3)$

Difference of Squares

• Difference of Squares Formula: $a^2 - b^2 = (a + b)(a - b)$
• Factoring: $a^2 - b^2 = (a + b)(a - b)$
• Example: Factor $x^2 - 9$
  • $x^2 - 9 = (x + 3)(x - 3)$

Sum and Difference Formulas

• The Sum of Cubes Formula is: $a^3 + b^3 = (a + b)(a^2 - ab + b^2)$
• The Difference of Cubes Formula is: $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$

Factoring Out Greatest Common Factors (GCF)

• The GCF is the largest number or expression that divides all terms of the polynomial
• Steps to factor out the GCF are:
  • Find the GCF of all terms
  • Divide each term by the GCF
  • Write the result as a product of the GCF and the remaining terms
• Example: Factoring $6x^2 + 12x + 18$ involves finding the GCF as 6, then writing it as $6(x^2 + 2x + 3)$

Difference of Squares

• The Difference of Squares Formula is: $a^2 - b^2 = (a + b)(a - b)$
• Factoring $a^2 - b^2$ results in $(a + b)(a - b)$
• Example: Factoring $x^2 - 9$ results in $(x + 3)(x - 3)$