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

Rewrite the middle term using these two numbers: \(x^{2}+8x - 2x - 16\).
Group the terms: \((x^{2}+8x)+(-2x - 16)\).
Factor out the common factors from each group: \(x(x + 8)-2(x + 8)\).
Now factor out the common binomial factor \((x + 8)\): \((x + 8)(x - 2)\).

Answer:

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