Subtracting Polynomials:
Subtracting polynomials involves combining like terms to simplify the expression. In this case, we are subtracting \(4x^2 - 7x - 13\) from \(3x^2 + 5x - 11\).

Step 1: Distribute the negative sign
To subtract a polynomial, distribute the negative sign to each term inside the parentheses of the polynomial being subtracted. This changes the signs of each term.
\(3x^2 + 5x - 11 - (4x^2 - 7x - 13)\)
\(= 3x^2 + 5x - 11 - 4x^2 + 7x + 13\)

Step 2: Combine like terms
Combine like terms by adding or subtracting coefficients of the same variables.
\(3x^2 - 4x^2 = -x^2\)
\(5x + 7x = 12x\)
\(-11 + 13 = 2\)

Step 3: Write the final answer
Combine the results from Step 2 to write the final simplified expression.
\(-x^2 + 12x + 2\)
Therefore, the result of subtracting \(4x^2 - 7x - 13\) from \(3x^2 + 5x - 11\) is \(-x^2 + 12x + 2\).

3x^2 - 5x -11 - 4x^2 -7x -13
= 1x^2 -12x -24