The purpose of factoring such functions is to then be able to solve equations of polynomials. For example, the solution to x^2 + 5x + 4 = 0 are the roots of x^2 + 5x + 4, namely, -1 and -4. Being able to find the roots of such polynomials is basic to solving problems in science classes in the following 2 to 3 years.
Factoring is a common mathematical process used to break down the factors, or numbers, that multiply together to form another number. Some numbers have multiple factors. The number 24, for instance, results when you multiply the factors of 6 and 4, 8 and 3, 12 and 2, and 24 and 1.