Factor completely.4, x, squared, minus, 12, x, minus, 1604x 2 −12x−160

Sure, let's factor the given expression step by step:

The given expression is 4x^2 - 12x - 160.

Step 1: First, we can factor out the greatest common factor (GCF) from each term. The GCF of 4, 12, and 160 is 4. So, we get:

4(x^2 - 3x - 40)

Step 2: Now, we need to factor the quadratic expression inside the parentheses. We are looking for two numbers that multiply to -40 (the constant term) and add to -3 (the coefficient of x). The numbers -8 and 5 satisfy these conditions. So, we can write:

4(x - 8)(x + 5)

So, the expression 4x^2 - 12x - 160 factors completely to 4(x - 8)(x + 5).