Question

factor completely.
2h² + 28h + 80

Explanation:

Step1: Factor out the GCF

The greatest common factor (GCF) of \(2h^2\), \(28h\), and \(80\) is \(2\). So we factor out \(2\) from each term:
\(2h^2 + 28h + 80 = 2(h^2 + 14h + 40)\)

Step2: Factor the quadratic trinomial

We need to factor \(h^2 + 14h + 40\). We look for two numbers that multiply to \(40\) and add up to \(14\). The numbers \(10\) and \(4\) work because \(10\times4 = 40\) and \(10 + 4 = 14\). So we can write:
\(h^2 + 14h + 40=(h + 10)(h + 4)\)

Step3: Combine the factors

Putting it all together, the completely factored form of \(2h^2 + 28h + 80\) is:
\(2(h + 10)(h + 4)\)

Answer:

\(2(h + 10)(h + 4)\)