Subtract 7x^2 + 4x - 9 from 5x^2 + 10x - 5.

Question

Express the result as a trinomial in descending degree order.

Answer 1

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:

1. Combine the \( x^2 \) terms: \[ 5x^2 - 7x^2 = -2x^2 \]

2. Combine the \( x \) terms: \[ 10x - 4x = 6x \]

3. 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:

\[ \boxed{-2x^2 + 6x + 4} \]