To subtract \( 7x^2 + 4x - 9 \) from \( 5x^2 + 10x - 5 \), we need to perform the operation:
\[ (5x^2 + 10x - 5) - (7x^2 + 4x - 9) \]
Distributing the negative sign to the second polynomial:
\[ 5x^2 + 10x - 5 - 7x^2 - 4x + 9 \]
Now we can combine like terms:
-
Combine the \( x^2 \) terms: \[ 5x^2 - 7x^2 = -2x^2 \]
-
Combine the \( x \) terms: \[ 10x - 4x = 6x \]
-
Combine the constant terms: \[ -5 + 9 = 4 \]
Putting it all together, we have:
\[ -2x^2 + 6x + 4 \]
Thus, the result expressed as a trinomial in descending degree order is:
\[ \boxed{-2x^2 + 6x + 4} \]