The process of factoring a real number involves expressing the number as a product of prime factors. Because a prime number has only two factors, the number 1 and the prime number itself, they are considered to be irreducible factors. Similarly, one factors a polynomial expression by representing it as a product of irreducible polynomials, i.e., polynomials that cannot be further reduced into other factors aside from the number 1 and itself.

EX.
12 = 2 × 2 × 3

x² + x = x (x + 1)

15x²y + 18xy² = 3xy (5x + 6y)

x³ + 5x² = x² (x + 5)

xy + 2y + 7x + 14
= y(x + 2) + 7(x + 2)
= (y + 7) (x + 2)