How can we check the binomial factors to verify that they are truly factors? are the factors (x + 5)(x – 8) truly factors of x2 – 2x – 30. show your work.

They are not. The easiest way to tell this is by multiplying the last number of each parenthesis together. This should always result in the last number in the equation. However, -8*5 does not equal -30, so these are not the true factors. 

You verify your answer by using the F.O.I.L. method. First Outside Inside Last. This shows that (x+5) & (x-8) is not the correct factors for 2x-2x-30 or x2-2x-30. Either way, the factors are not right for either of those equations. Hope my answer helps you