Question

1. ( x^2 - 12x + 32 )

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(32\) and add up to \(-12\). The numbers are \(-8\) and \(-4\) since \((-8)\times(-4) = 32\) and \((-8)+(-4)=-12\).

Step2: Factor the quadratic

Using the numbers from Step 1, we can factor \(x^{2}-12x + 32\) as \((x - 8)(x - 4)\).

Answer:

\((x - 8)(x - 4)\)