Let's analyze the given polynomial [tex]\( -2x^2 - x + 2 \)[/tex].
### Step-by-Step Solution:
1. Identify the terms of the polynomial:
The polynomial contains three terms:
[tex]\[
-2x^2, \quad -x, \quad \text{and} \quad 2
\][/tex]
2. Determine the degree of the polynomial:
The degree of a polynomial is the highest power of the variable [tex]\( x \)[/tex] that appears in the polynomial.
- The first term is [tex]\( -2x^2 \)[/tex] and has a power of [tex]\( 2 \)[/tex].
- The second term is [tex]\( -x \)[/tex] and has a power of [tex]\( 1 \)[/tex].
- The third term is [tex]\( 2 \)[/tex] and can be considered as [tex]\( 2x^0 \)[/tex] with a power of [tex]\( 0 \)[/tex].
Therefore, the highest power of [tex]\( x \)[/tex] among the terms is [tex]\( 2 \)[/tex], so the degree of the polynomial is [tex]\( 2 \)[/tex].
3. Classify the polynomial:
Polynomials are classified based on their degree:
- A polynomial of degree [tex]\( 1 \)[/tex] is called a linear polynomial.
- A polynomial of degree [tex]\( 2 \)[/tex] is called a quadratic polynomial.
- A polynomial of degree [tex]\( 3 \)[/tex] is called a cubic polynomial.
- And so on.
Since the degree of the polynomial [tex]\( -2x^2 - x + 2 \)[/tex] is [tex]\( 2 \)[/tex], it is classified as a quadratic polynomial.
### Conclusion:
The polynomial [tex]\( -2x^2 -x + 2 \)[/tex] is a quadratic polynomial with a degree of 2.
