Factorize x² – 8x + 15also provide explanation and correct will give

x² – 8x + 15

(x-3) (x-5)

what two numbers multiply to 15 and add to -8

I list all the factor of 15 that are negative and see if they add to -8

-1 * -15  = 15      -1 + -15 = -16   no

-3 * -5  = 15      -3 + -5 = -8  works

the barter