Is the binomial x-9 a factor of 4x^3-28^2-36x-27

No

Step-by-step explanation:

If (x - 9) is a factor then x = 9 is a root and f (9) = 0

f (x) = 4x³ - 28x² - 36x - 27, hence

f (9) = 4 (9) ³ - 28 (9) ² - 36 (9) - 27

= 2916 - 2268 - 324 - 27 = 297

Since f (9) ≠ 0 then (x - 9) is not a factor of f (x)