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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!

Factor the quadratic expression x^2 - 4x - 21.

Learn how to factor the quadratic expression x^2 - 4x - 21 step-by-step. This algebra problem demonstrates how to factor trinomials by finding two numbers that multiply to the constant and sum to the middle coefficient. Ideal for students in Grades 8-10.

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