Factor Quadratic 04D914

1. Let's look at the problem: we want to understand the expression $x^2 + 7x + 12$. 2. This is a quadratic expression, which means it has a term with $x^2$, a term with $x$, and a constant number. 3. The goal is to factor it, which means to write it as two simpler expressions multiplied together. 4. We look for two numbers that multiply to $12$ (the constant) and add up to $7$ (the coefficient of $x$). 5. The numbers $3$ and $4$ work because $3 \times 4 = 12$ and $3 + 4 = 7$. 6. So, we can write $x^2 + 7x + 12$ as $(x + 3)(x + 4)$. 7. This means if you multiply $(x + 3)$ by $(x + 4)$, you get back the original expression. 8. Factoring helps us solve equations and understand expressions better!