Question

Which of the binomials below is a factor of this trinomial?

x^2 + 4x - 60

Answer 1

(x+10)(x-6)

Answer 2

You don't list the "binomials below" in your question, but you can proceed as follows.

Suppose x-6 is listed as a possible answer. That is zero if x = 6. So plug x=6 into the original x^2 + 4x - 60 to get 6^2 + 4*6 - 60 = 36 + 24 -60 = 0. hence x-6 is a factor.

On the other hand, x-5 is not a factor, because plugging x=5 into does not work.