To classify the polynomial [tex]\(-2x^2 - x + 2\)[/tex] and determine its degree, follow these steps:
1. Identify the terms in the polynomial:
The given polynomial is [tex]\(-2x^2 - x + 2\)[/tex]. This polynomial consists of three terms: [tex]\(-2x^2\)[/tex], [tex]\(-x\)[/tex], and [tex]\(2\)[/tex].
2. Determine the degree of the polynomial:
The degree of a polynomial is the highest power of the variable [tex]\(x\)[/tex] in the polynomial. Let's analyze each term:
- The term [tex]\(-2x^2\)[/tex] has a degree of [tex]\(2\)[/tex] because the exponent of [tex]\(x\)[/tex] is [tex]\(2\)[/tex].
- The term [tex]\(-x\)[/tex] has a degree of [tex]\(1\)[/tex] because the exponent of [tex]\(x\)[/tex] is [tex]\(1\)[/tex].
- The term [tex]\(2\)[/tex] is a constant and has a degree of [tex]\(0\)[/tex] because it has no [tex]\(x\)[/tex] term.
The highest degree among these terms is [tex]\(2\)[/tex]. Therefore, the degree of the polynomial [tex]\(-2x^2 - x + 2\)[/tex] is [tex]\(2\)[/tex].
3. Classify the polynomial:
Polynomial classification is based on the degree of the polynomial:
- A polynomial of degree [tex]\(0\)[/tex] is called a constant polynomial.
- 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 this polynomial is [tex]\(2\)[/tex], it is classified as a quadratic polynomial.
Therefore, the polynomial [tex]\(-2x^2 - x + 2\)[/tex] is a Quadratic polynomial with a degree of 2.
So, the completed statement is:
The polynomial [tex]\(-2x^2 - x + 2\)[/tex] is a Quadratic with a degree of 2.
