Question

factor completely.
$2u^2 - 26u - 60$

Explanation:

Step1: Factor out the GCF

The greatest common factor (GCF) of \(2u^2\), \(-26u\), and \(-60\) is \(2\). So we factor out \(2\) from each term:
\(2u^2 - 26u - 60 = 2(u^2 - 13u - 30)\)

Step2: Factor the quadratic trinomial

We need to factor \(u^2 - 13u - 30\). We look for two numbers that multiply to \(-30\) and add up to \(-13\). The numbers are \(-15\) and \(2\) because \(-15\times2=-30\) and \(-15 + 2=-13\). So we can factor the quadratic as:
\(u^2 - 13u - 30=(u - 15)(u + 2)\)

Step3: Combine the factors

Putting it all together, we have:
\(2u^2 - 26u - 60 = 2(u - 15)(u + 2)\)

Answer:

\(2(u - 15)(u + 2)\)