Question

x² + 6x - 16

Explanation:

Step1: Find two numbers

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

Step2: Rewrite the middle term

Rewrite the middle term \(6x\) as \(8x-2x\) in the quadratic expression:
\(x^{2}+8x - 2x-16\)

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

Answer:

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