Question

factor completely.
$2u^{2} + 48u - 50$

Explanation:

Step1: Factor out the GCF

First, find the greatest common factor (GCF) of the terms \(2u^2\), \(48u\), and \(-50\). The GCF of 2, 48, and 50 is 2. Factor out 2 from each term:
\(2u^2 + 48u - 50 = 2(u^2 + 24u - 25)\)

Step2: Factor the quadratic trinomial

Now, factor the quadratic trinomial \(u^2 + 24u - 25\). We need two numbers that multiply to \(-25\) and add up to \(24\). The numbers are 25 and \(-1\) because \(25 \times (-1) = -25\) and \(25 + (-1) = 24\). So, we can factor \(u^2 + 24u - 25\) as \((u + 25)(u - 1)\).

Step3: Combine the factors

Putting it all together, the completely factored form of \(2u^2 + 48u - 50\) is:
\(2(u + 25)(u - 1)\)

Answer:

\(2(u + 25)(u - 1)\)