Question

Factor completely. x^2−8x+15

Answer 1

Answer:

(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)