Question

factor completely. \\( w^2 + 5w + 4 \\)

Explanation:

Step1: Find two numbers that multiply to 4 and add to 5.

We need two numbers \(a\) and \(b\) such that \(a\times b = 4\) and \(a + b=5\). The numbers 1 and 4 work because \(1\times4 = 4\) and \(1 + 4=5\).

Step2: Rewrite the middle term using these numbers.

\(w^{2}+5w + 4=w^{2}+w+4w + 4\)

Step3: Group the terms and factor out the greatest common factor (GCF) from each group.

Group the first two terms and the last two terms: \((w^{2}+w)+(4w + 4)\)
Factor out \(w\) from the first group and 4 from the second group: \(w(w + 1)+4(w + 1)\)

Step4: Factor out the common binomial factor.

Now we can factor out \((w + 1)\) from both terms: \((w + 1)(w + 4)\)

Answer:

\((w + 1)(w + 4)\)