Factor completely.

x^2-8x+15

(x-3) (x-5)

Step-by-step explanation:

x²-8x+15

note that the constant term is 15 and the x-coefficient is - 8

step 1: List factors of 15 : ±1, ±3, ±5, ±15

step 2: observe the factors listed and ask ourselves the following questions:

1) What 2 factors in the list, when multiplied gives the constant 15

2) What same 2 factors when added gives the x-coefficient - 8

by deduction or trial and error, we can see that - 3 and - 5, when multiplied gives 15 and when added gives - 8. Hence these become the factors.

Hence the factors are

(x-3) (x-5)