Question

x² + 6x - 16

Explanation:

Step1: Find two numbers

We need two numbers that multiply to -16 and add up to 6. The numbers are 8 and -2 since \(8\times(-2)= -16\) and \(8+(-2)=6\).

Step2: Factor the quadratic

Using the numbers from Step 1, we can rewrite the middle term and factor by grouping:
\[

$$\begin{align*} x^{2}+6x - 16&=x^{2}+8x-2x - 16\\ &=x(x + 8)-2(x + 8)\\ &=(x + 8)(x - 2) \end{align*}$$

\]

Answer:

\((x + 8)(x - 2)\)