Question

factor completely.
$2x^2 - 2x - 60$

Explanation:

Step1: Factor out the GCF

The greatest common factor (GCF) of \(2x^2\), \(-2x\), and \(-60\) is 2. So we factor out 2:
\(2x^2 - 2x - 60 = 2(x^2 - x - 30)\)

Step2: Factor the quadratic

We need to factor \(x^2 - x - 30\). We look for two numbers that multiply to \(-30\) and add to \(-1\). The numbers are \(-6\) and \(5\) because \((-6)\times5=-30\) and \(-6 + 5=-1\). So we can factor the quadratic as:
\(x^2 - x - 30=(x - 6)(x + 5)\)

Step3: Combine the factors

Putting it all together, the completely factored form of \(2x^2 - 2x - 60\) is:
\(2(x - 6)(x + 5)\)

Answer:

\(2(x - 6)(x + 5)\)