Factoring Polynomials

A Review Of Some Concepts (for myself):
Remainder Theorem:
When dividing a polynomial expression p(x) by a linear polynomial expression x-b, the remainder is p(b).

Factor Theorem:
A linear expression x-b is only a factor of p(x) if p(b) is 0. (So there must not be any remainder)

Integral Zero Theorem:
If x=b is an integral zero of the polynomial P(x), then the constant term of P(x) must be divisible by 2.

Rational Zero Theorem:
If x=b/a is a rational zero of the polynomial P(x), then the constant term of P(x) must be divisible by b, and the leading coefficient must be divisible by a.