Question

factor completely.
$5n^2 + 40n + 35$

Explanation:

Step1: Factor out the GCF

First, find the greatest common factor (GCF) of the terms \(5n^2\), \(40n\), and \(35\). The GCF of 5, 40, and 35 is 5. So we factor out 5:
\(5n^2 + 40n + 35 = 5(n^2 + 8n + 7)\)

Step2: Factor the quadratic trinomial

Now, factor the quadratic trinomial \(n^2 + 8n + 7\). We need two numbers that multiply to 7 and add up to 8. Those numbers are 1 and 7. So we can factor it as:
\(n^2 + 8n + 7 = (n + 1)(n + 7)\)

Step3: Combine the factors

Putting it all together, the completely factored form of the original expression is:
\(5(n + 1)(n + 7)\)

Answer:

\(5(n + 1)(n + 7)\)