Question

Is x + 5 one of the factors for 4x^2 – 8x – 140 ?

Answer 1

Yup. You are correct.
4x^2 - 8x - 140 = 4(x^2 - 2x - 35) = 4(x - 7)(x + 5)

Answer 2

You can use the factor theorem to check it.
Consider the factor (x+5),
f(-5) = 4(-5)^2 – 8(-5) – 140 = 0
Therefore, (x+5) is a factor of 4x^2 – 8x – 140 .