To classify the polynomial [tex]\( -2x^2 - x + 2 \)[/tex] and determine its degree, follow these steps:
1. Identify the degree of the polynomial:
- The degree of a polynomial is determined by the highest exponent of the variable [tex]\( x \)[/tex].
- In the polynomial [tex]\( -2x^2 - x + 2 \)[/tex], the term with the highest exponent is [tex]\( -2x^2 \)[/tex].
- The exponent of [tex]\( x \)[/tex] in [tex]\( -2x^2 \)[/tex] is 2.
2. Determine the degree:
- Therefore, the degree of the polynomial is 2.
3. Classify the polynomial:
- Polynomials are classified based on their degree:
- A polynomial of degree 0 is called a "constant".
- A polynomial of degree 1 is called "linear".
- A polynomial of degree 2 is called "quadratic".
- A polynomial of degree 3 is called "cubic".
- And so on for higher degrees.
- Since the degree of the polynomial is 2, it is classified as a "quadratic" polynomial.
Summarizing this:
The polynomial [tex]\( -2x^2 - x + 2 \)[/tex] is a quadratic polynomial with a degree of 2.
