Subtract two polynomials

1. Distribute the negative sign: The expression involves subtracting the second polynomial from the first. This means we need to distribute the negative sign to each term in the second polynomial. So, $-( -9x^2 - 3x - 4 )$ becomes $+9x^2 + 3x + 4$. The expression is now $10x^2 + 8x - 5 + 9x^2 + 3x + 4$.
2. Group like terms: Combine terms with the same power of $x$. Group the $x^2$ terms, the $x$ terms, and the constant terms together.
$$(10x^2 + 9x^2) + (8x + 3x) + (-5 + 4)$$
3. Combine like terms: Perform the addition and subtraction for each group of like terms.
For the $x^2$ terms: $10x^2 + 9x^2 = 19x^2$
For the $x$ terms: $8x + 3x = 11x$
For the constant terms: $-5 + 4 = -1$
4. Write the simplified expression: Combine the results from the previous step to form the final simplified polynomial.
$$19x^2 + 11x - 1$$