To simplify the given expression [tex]\(\left(8x^2 + 3x\right) - \left(12x^2 - 1\right)\)[/tex], follow these steps:
1. Distribute the Negative Sign: When subtracting polynomials, distribute the negative sign to each term inside the second set of parentheses.
[tex]\[
(8x^2 + 3x) - (12x^2 - 1) = 8x^2 + 3x - 12x^2 + 1
\][/tex]
2. Combine Like Terms: Group like terms together and perform the necessary addition or subtraction.
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(8x^2 - 12x^2\)[/tex]
- Combine the constant terms and linear terms: [tex]\(3x + 1\)[/tex]
[tex]\[
(8x^2 - 12x^2) + 3x + 1 = -4x^2 + 3x + 1
\][/tex]
3. Identify the Classification:
- The simplified polynomial, [tex]\(-4x^2 + 3x + 1\)[/tex], has three terms. A polynomial with three terms is called a "trinomial."
- The highest exponent of [tex]\(x\)[/tex] in the polynomial is 2, which means it is of the second degree, or "quadratic."
Given these points, the simplified expression [tex]\(-4x^2 + 3x + 1\)[/tex] is a quadratic trinomial.
Thus, the correct answer is:
C. quadratic trinomial
