Question

factor completely.
$4g^2 + 8g - 60$

Explanation:

Step1: Factor out the GCF

First, find the greatest common factor (GCF) of the terms \(4g^2\), \(8g\), and \(-60\). The GCF of 4, 8, and 60 is 4. So we factor out 4:
\(4g^2 + 8g - 60 = 4(g^2 + 2g - 15)\)

Step2: Factor the quadratic trinomial

Now, factor the quadratic \(g^2 + 2g - 15\). We need two numbers that multiply to \(-15\) and add up to \(2\). The numbers are \(5\) and \(-3\) because \(5 \times (-3) = -15\) and \(5 + (-3) = 2\). So we can write:
\(g^2 + 2g - 15 = (g + 5)(g - 3)\)

Step3: Combine the factors

Putting it all together, the completely factored form is:
\(4(g + 5)(g - 3)\)

Answer:

\(4(g + 5)(g - 3)\)