Factoring

Procedures for factoring are illustrated below.

1. Look for a common factor.
2. To factor a quadratic of the form $x^{2} + bx+ c$, look for two real numbers $p$ and $q$ satisfying $p+q=b$ and $pq=c$.
3. To factor a quadratic of the form $ax^{2} + bx + c$ where $a \neq 0$ and $a\neq1$ quickly, use the guess and check method illustrated in the video.
4. To factor a difference of squares, use conjugate pairs: $x^{2} - p^{2} = (x+p)(x-p)$.
   A sum of two squares does not factor over the real numbers.
5. To factor a sum or difference of cubes, use the factoring formulas below.
   The trinomial you obtain by factoring a sum or difference of cubes does not factor further.
   1. $x^{3} + p^{3} = (x+p)(x^{2}-px+p^{2})$
   2. $x^{3} - p^{3} = (x-p)(x^{2}+px+p^{2})$
6. More techniques for factoring general polynomial functions are given in Chapter 3.