To simplify the expression [tex]\(\left(3x^2 - 11x - 4\right) - \left(2x^2 - x - 6\right)\)[/tex] and determine the classification of the resulting polynomial, let's proceed step-by-step.
### Step 1: Distribute the Negative Sign:
We need to distribute the negative sign through the second polynomial:
[tex]\[
\left(3x^2 - 11x - 4\right) - \left(2x^2 - x - 6\right)
\][/tex]
This can be rewritten as:
[tex]\[
3x^2 - 11x - 4 - 2x^2 + x + 6
\][/tex]
### Step 2: Combine Like Terms:
Now, we need to combine like terms. Group the terms involving [tex]\(x^2\)[/tex], [tex]\(x\)[/tex], and the constant terms separately.
[tex]\[
(3x^2 - 2x^2) + (-11x + x) + (-4 + 6)
\][/tex]
### Step 3: Simplify Each Group:
Simplify each group of like terms:
[tex]\[
(3x^2 - 2x^2) = x^2
\][/tex]
[tex]\[
(-11x + x) = -10x
\][/tex]
[tex]\[
(-4 + 6) = 2
\][/tex]
### Step 4: Form the Simplified Expression:
Combine the simplified terms:
[tex]\[
x^2 - 10x + 2
\][/tex]
### Step 5: Determine the Classification of the Polynomial:
Now, we analyze the simplified polynomial [tex]\(x^2 - 10x + 2\)[/tex]:
- The degree of this polynomial is 2 (since the highest power of [tex]\(x\)[/tex] is [tex]\(x^2\)[/tex]).
- The number of terms is 3 (specifically, [tex]\(x^2\)[/tex], [tex]\(-10x\)[/tex], and [tex]\(2\)[/tex]).
### Classification:
A polynomial with a degree of 2 (quadratic) and three terms (trinomial) is classified as a quadratic trinomial.
Therefore, the correct answer is:
[tex]\[
\boxed{\text{A. quadratic trinomial}}
\][/tex]
