Question

$x^{2}+6x-16$

Explanation:

Step1: Identify factors of -16

Find two numbers that multiply to $-16$ and add to $6$: $8$ and $-2$ (since $8 \times (-2) = -16$, $8 + (-2) = 6$).

Step2: Factor the quadratic expression

Rewrite the quadratic using the two numbers 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:

$(x + 8)(x - 2)$