Question

factor completely.
2k² - 30k + 100

Explanation:

Step1: Factor out the GCF

First, find the greatest common factor (GCF) of the terms \(2k^2\), \(-30k\), and \(100\). The GCF of 2, 30, and 100 is 2. So we factor out 2:
\(2k^2 - 30k + 100 = 2(k^2 - 15k + 50)\)

Step2: Factor the quadratic

Now, factor the quadratic \(k^2 - 15k + 50\). We need two numbers that multiply to 50 and add up to -15. The numbers -5 and -10 work because \((-5)\times(-10)=50\) and \((-5)+(-10)=-15\). So we can factor it as:
\(k^2 - 15k + 50=(k - 5)(k - 10)\)

Step3: Combine the factors

Putting it all together, the completely factored form is:
\(2(k - 5)(k - 10)\)

Answer:

\(2(k - 5)(k - 10)\)