The expression given in the image is:

$x^2 - 7x + 12$

To factor this quadratic expression, we need to find two numbers that multiply to $12$ (the constant term) and add up to $-7$ (the coefficient of the linear term).

These two numbers are $-3$ and $-4$, because:

$-3 \times -4 = 12 \quad \text{and} \quad -3 + (-4) = -7$

So, we can factor the quadratic as:

$x^2 - 7x + 12 = (x - 3)(x - 4)$

The factored form of $x^2 - 7x + 12$ is $(x - 3)(x - 4)$.

Would you like more details or have any questions? Here are some related questions:

1. How can you confirm the factorization by expanding the factors?
2. What method is used to factor quadratic expressions like this one?
3. How would you solve $x^2 - 7x + 12 = 0$ using the factored form?
4. What is the significance of the roots of the equation $x^2 - 7x + 12 = 0$?
5. How does the discriminant help in determining the type of roots a quadratic equation has?

Tip: When factoring quadratics, always check your factors by expanding them to ensure they match the original expression.