factor.\nh² + 5h + 4

Explanation:

Step1: Find two numbers

We need two numbers that multiply to 4 (the constant term) and add up to 5 (the coefficient of the middle - term). The numbers are 1 and 4 since (1\times4 = 4) and (1 + 4=5).

Step2: Rewrite the middle - term

Rewrite (5h) as (h + 4h). So, (h^{2}+5h + 4=h^{2}+h+4h + 4).

Step3: Group the terms

Group the terms: ((h^{2}+h)+(4h + 4)).

Step4: Factor out the common factors from each group

From the first group (h^{2}+h), we can factor out (h) to get (h(h + 1)). From the second group (4h + 4), we can factor out 4 to get (4(h + 1)).

Step5: Factor out the common binomial factor

We have (h(h + 1)+4(h + 1)=(h + 1)(h + 4)).

Answer:

((h + 1)(h + 4))