1. Let's start by stating the problem: factoring a function means expressing it as a product of simpler functions or polynomials. 2. The most common type of factoring is factoring polynomials. For example, consider the quadratic function $f(x) = x^2 + 5x + 6$. 3. The formula to factor a quadratic polynomial $ax^2 + bx + c$ is to find two numbers that multiply to $ac$ and add to $b$. 4. For $f(x) = x^2 + 5x + 6$, $a=1$, $b=5$, and $c=6$. We need two numbers that multiply to $1 \times 6 = 6$ and add to $5$. 5. These numbers are $2$ and $3$ because $2 \times 3 = 6$ and $2 + 3 = 5$. 6. We rewrite the middle term using these numbers: $x^2 + 2x + 3x + 6$. 7. Now, group terms: $(x^2 + 2x) + (3x + 6)$. 8. Factor each group: $x(x + 2) + 3(x + 2)$. 9. Factor out the common binomial: $(x + 2)(x + 3)$. 10. So, the factored form of $f(x) = x^2 + 5x + 6$ is $$f(x) = (x + 2)(x + 3)$$. Factoring helps simplify expressions and solve equations more easily.