Answer: x + 10` is **not** a factor of `f(x) = 5x^3 + 60x^2 + 109x + 90`.
Step-by-step explanation: To determine if `x + 10` is a factor of `f(x) = 5x^3 + 60x^2 + 109x + 90`, we can use the Factor Theorem. The Factor Theorem states that if `f(a) = 0`, then `x - a` is a factor of `f(x)`.
In this case, we want to determine if `x + 10` is a factor of `f(x)`, so we can let `a = -10` and evaluate `f(-10)`:
`f(-10) = 5(-10)^3 + 60(-10)^2 + 109(-10) + 90`
`= -5000 + 6000 - 1090 + 90`
`= -1000`
Since `f(-10) ≠ 0`, we can conclude that `x + 10` is **not** a factor of `f(x) = 5x^3 + 60x^2 + 109x + 90`.