Question

factor completely.
$k^2 + 20k + 19$
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Explanation:

Step1: Identify factors of 19

We need two numbers that multiply to 19 and add up to 20. The factors of 19 are 1 and 19 (since 19 is a prime number).

Step2: Factor the quadratic

Using the form \(k^2 + (a + b)k + ab=(k + a)(k + b)\), where \(a = 1\) and \(b = 19\) (because \(1\times19 = 19\) and \(1+19 = 20\)). So, \(k^2+20k + 19=(k + 1)(k + 19)\).

Answer:

\((k + 1)(k + 19)\)