Question

$x^2 + 6x - 16$

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

Step4: Factor out the common binomial

Factor out the common binomial \((x + 8)\) to get \((x + 8)(x - 2)\).

Answer:

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