1. The problem is to factor the second expression given by the user. Since the user did not provide the expressions explicitly, I will assume a typical example for demonstration: factor the quadratic expression $x^2 + 5x + 6$. 2. The formula used for factoring a quadratic expression $ax^2 + bx + c$ is to find two numbers that multiply to $ac$ and add to $b$. 3. For $x^2 + 5x + 6$, $a=1$, $b=5$, and $c=6$. We need two numbers that multiply to $1 \times 6 = 6$ and add to $5$. 4. The numbers $2$ and $3$ satisfy this because $2 \times 3 = 6$ and $2 + 3 = 5$. 5. Rewrite the middle term using these numbers: $x^2 + 2x + 3x + 6$. 6. Group terms: $(x^2 + 2x) + (3x + 6)$. 7. Factor each group: $x(x + 2) + 3(x + 2)$. 8. Factor out the common binomial: $(x + 2)(x + 3)$. 9. Therefore, the factored form of $x^2 + 5x + 6$ is $(x + 2)(x + 3)$. This method can be applied to any quadratic expression where $a=1$.