Question

factor completely.
2h² - 64h + 62

Explanation:

Step1: Factor out the GCF

The greatest common factor (GCF) of \(2h^2\), \(-64h\), and \(62\) is \(2\). So we factor out \(2\) from each term:
\(2h^2 - 64h + 62 = 2(h^2 - 32h + 31)\)

Step2: Factor the quadratic trinomial

We need to find two numbers that multiply to \(31\) (the constant term) and add up to \(-32\) (the coefficient of the middle term). The numbers are \(-1\) and \(-31\) because \((-1)\times(-31)=31\) and \((-1)+(-31)=-32\). So we can factor \(h^2 - 32h + 31\) as \((h - 1)(h - 31)\).
Putting it all together, the completely factored form is \(2(h - 1)(h - 31)\).

Answer:

\(2(h - 1)(h - 31)\)