We are given:
\(\displaystyle{x}^{{2}}+{8}{x}+{15}\)

To factor trinomials in the form \(\displaystyle{x}^{{2}}+{b}{x}+{c}\), think of two factors of c (which are m and n) that add to b so that it factors to (x+m)(x+n).

Here, think of two factors of 15 that when added, the result is 8. These are 3 and 5 so we can factor the trinomial as: (x+3)(x+5)

To factor trinomials in the form \(\displaystyle{x}^{{2}}+{b}{x}+{c}\), think of two factors of c (which are m and n) that add to b so that it factors to (x+m)(x+n).

Here, think of two factors of 15 that when added, the result is 8. These are 3 and 5 so we can factor the trinomial as: (x+3)(x+5)