x2+8x+15

We are given: ${\displaystyle x^2+8x+15}$
To factor trinomials in the form ${\displaystyle x^2+bx+c}$, 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)