Question

x² - 4x - 21

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(-21\) and add up to \(-4\). Let's list the factor pairs of \(-21\): \((-7, 3)\) because \(-7\times3 = -21\) and \(-7 + 3=-4\).

Step2: Factor the quadratic

Using the numbers we found, we can rewrite the middle term of the quadratic \(x^{2}-4x - 21\) as \(x^{2}-7x+3x - 21\). Then we factor by grouping:
\[

$$\begin{align*} x^{2}-7x + 3x-21&=x(x - 7)+3(x - 7)\\ &=(x - 7)(x + 3) \end{align*}$$

\]

Answer:

\((x - 7)(x + 3)\)