Question

factor completely.
4w² + 4w - 48

Explanation:

Step1: Factor out the GCF

First, find the greatest common factor (GCF) of the terms \(4w^2\), \(4w\), and \(-48\). The GCF of 4, 4, and 48 is 4. So we factor out 4:
\(4w^2 + 4w - 48 = 4(w^2 + w - 12)\)

Step2: Factor the quadratic

Now, factor the quadratic \(w^2 + w - 12\). We need two numbers that multiply to \(-12\) and add to \(1\). The numbers are \(4\) and \(-3\) because \(4 \times (-3) = -12\) and \(4 + (-3) = 1\). So we can write:
\(w^2 + w - 12 = (w + 4)(w - 3)\)

Step3: Combine the factors

Putting it all together, the completely factored form is:
\(4(w + 4)(w - 3)\)

Answer:

\(4(w + 4)(w - 3)\)