To simplify the expression [tex]\((3x^2 - 11x - 4) - (2x^2 - x - 6)\)[/tex], we need to subtract the corresponding coefficients of the polynomials.
First, write down the given polynomials:
[tex]\[
3x^2 - 11x - 4 \quad \text{and} \quad 2x^2 - x - 6
\][/tex]
Now, perform the subtraction term by term:
1. For the [tex]\(x^2\)[/tex] terms:
[tex]\[
3x^2 - 2x^2 = 1x^2
\][/tex]
2. For the [tex]\(x\)[/tex] terms:
[tex]\[
-11x - (-x) = -11x + x = -10x
\][/tex]
3. For the constant terms:
[tex]\[
-4 - (-6) = -4 + 6 = 2
\][/tex]
Putting it all together, the resulting polynomial is:
[tex]\[
1x^2 - 10x + 2
\][/tex]
This polynomial is a second-degree polynomial (the highest power of [tex]\(x\)[/tex] is 2) with three terms: [tex]\(x^2\)[/tex], [tex]\(x\)[/tex], and the constant term. Therefore, it is classified as a quadratic trinomial.
Thus, the correct answer is:
[tex]\[
\boxed{\text{A. quadratic trinomial}}
\][/tex]
