factoring by grouping

5x^2
//// 25                           5x times x              2x^2+6x
///                                                  2x(x+3)
5x5
25x1

GCF: largest value that can go into each term of an expression or set of numbers

3x(4x-5)+5(4x-5)
(4x-5) gcf

ax^2+bx+c

a: leading coefficent
b: middle term coefficent
c:constant

look for integers (r and s) such that rxs=c and r+s+b so that the factored expression looks like such
(x+r)(x+s)