Factoring Checklist for Young RSGC Mathematicians...

1. Common Factors: `ax+ay=a*(x+y)`
2. Factor by Grouping (4 terms): `ax+ay+bx+by = a*(x+y)+b*(x+y)` `\ \ = (x+y)*(a+b)`
3. Patterns:
   • Difference of Squares: `a^2-b^2=(a+b)*(a-b)`
   • (Disguised) Difference of Squares: `x-y=(sqrt(x)+sqrt(y))*(sqrt(x)-sqrt(y))`
   • Sum or Difference of Cubes: `a^3+-b^3=(a+-b)(a^2+-ab+b^2)`
   • Difference of nth's: `a^n-b^n = (a-b)(a^{n-1}+a^{n-2}b+cdots+ab^{n-2}+b^{n-1})`
   • Sum of odd nth's: `a^n+b^n = (a+b)(a^{n-1}-a^{n-2}b+cdots-ab^{n-2}+b^{n-1})`
   • Square of a Binomial: `a^2+-2ab+b^2=(a+-b)^2`
4. Quadratic trinomials: `ax^2+bx+c`. Find two numbers with a sum of `b` and a product of `ac`.