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:
\(x^{2}+8x - 2x - 16\)
Then, group the terms:
\((x^{2}+8x)+(-2x - 16)\)
Factor out the greatest common factor from each group:
\(x(x + 8)-2(x + 8)\)
Now, factor out the common binomial factor \((x + 8)\):
\((x + 8)(x - 2)\)

Answer:

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