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: Rewrite the middle term

Rewrite the quadratic expression \(x^{2}+6x - 16\) as \(x^{2}+8x-2x - 16\).

Step3: Group and factor

Group the first two terms and the last two terms: \((x^{2}+8x)+(-2x - 16)\). Factor out the greatest common factor from each group: \(x(x + 8)-2(x + 8)\). Then factor out the common binomial factor \((x + 8)\): \((x + 8)(x-2)\).

Answer:

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