The expression given is a quadratic trinomial:

$x^2 - 4x - 21$

Let's try to factor this expression.

We need two numbers that multiply to $-21$ (the constant term) and add to $-4$ (the coefficient of the linear term).

The factors of $-21$ are: $1 \times (-21),\quad 3 \times (-7)$

From these, we see that $3 + (-7) = -4$. So, the correct factorization is:

$(x + 3)(x - 7)$

Thus, the factored form of $x^2 - 4x - 21$ is:

$(x + 3)(x - 7)$

Let me know if you'd like more details or have any questions!

Here are 5 related questions for further practice:

1. How would you factor $x^2 + 6x - 27$?
2. Can you factor $x^2 - 10x + 25$?
3. What is the solution to $x^2 - 4x - 21 = 0$?
4. How can you factor a quadratic when the leading coefficient is not 1?
5. What are the roots of $x^2 + 5x + 6$?

Tip: When factoring quadratic trinomials, look for pairs of factors that not only multiply to the constant term but also sum up to the coefficient of the middle term!