Alright, let's classify the polynomial [tex]\(5x^2 + 4x - 2\)[/tex].
### Step 1: Identify the Degree
The degree of a polynomial is the highest power of the variable [tex]\(x\)[/tex] in the polynomial.
In the polynomial [tex]\(5x^2 + 4x - 2\)[/tex]:
- The term [tex]\(5x^2\)[/tex] has a degree of 2 (since the exponent of [tex]\(x\)[/tex] is 2).
- The term [tex]\(4x\)[/tex] has a degree of 1 (since the exponent of [tex]\(x\)[/tex] is 1).
- The constant term [tex]\(-2\)[/tex] has a degree of 0 (since there is no [tex]\(x\)[/tex] present).
Therefore, the highest power of [tex]\(x\)[/tex] is 2, making the degree of the polynomial [tex]\(2\)[/tex].
### Step 2: Identify the Leading Coefficient
The leading coefficient is the coefficient of the term with the highest degree in the polynomial.
In the polynomial [tex]\(5x^2 + 4x - 2\)[/tex], the term with the highest degree is [tex]\(5x^2\)[/tex], and its coefficient is [tex]\(5\)[/tex].
Therefore, the leading coefficient is [tex]\(5\)[/tex].
### Step 3: Identify the Constant Term
The constant term in a polynomial is the term that does not contain any variables (i.e., it is a number by itself).
In the polynomial [tex]\(5x^2 + 4x - 2\)[/tex], the constant term is [tex]\(-2\)[/tex].
### Summary
To summarize the classification of the polynomial [tex]\(5x^2 + 4x - 2\)[/tex]:
1. Degree: The polynomial has a degree of [tex]\(2\)[/tex].
2. Leading Coefficient: The leading coefficient is [tex]\(5\)[/tex].
3. Constant Term: The constant term is [tex]\(-2\)[/tex].
So, the polynomial [tex]\(5x^2 + 4x - 2\)[/tex] has:
- Degree: [tex]\(2\)[/tex]
- Leading Coefficient: [tex]\(5\)[/tex]
- Constant Term: [tex]\(-2\)[/tex]
