To classify the given polynomial [tex]\(7x - 3x^2 - 4x + 5\)[/tex], let's follow these steps:
### Step 1: Simplify the Polynomial
Start by combining like terms:
[tex]\[ 7x - 3x^2 - 4x + 5 \][/tex]
Combine the [tex]\(x\)[/tex] terms:
[tex]\[ (7x - 4x) = 3x \][/tex]
So, the polynomial simplifies to:
[tex]\[ -3x^2 + 3x + 5 \][/tex]
### Step 2: Determine the Degree of the Polynomial
The degree of a polynomial is the highest power of [tex]\(x\)[/tex] in the expression. In the simplified polynomial:
[tex]\[ -3x^2 + 3x + 5 \][/tex]
The highest power of [tex]\(x\)[/tex] is [tex]\(2\)[/tex], hence the degree of the polynomial is [tex]\(2\)[/tex].
### Step 3: Count the Number of Terms
A polynomial term is either a constant or a product of a constant and one or more variables raised to a power. In the simplified polynomial:
[tex]\[ -3x^2 + 3x + 5 \][/tex]
We can see there are three terms:
1. [tex]\(-3x^2\)[/tex]
2. [tex]\(3x\)[/tex]
3. [tex]\(5\)[/tex]
So, there are 3 terms in the polynomial.
### Step 4: Classify the Polynomial
The classification of a polynomial is based on its degree and the number of terms it contains:
- Degree: [tex]\(2\)[/tex] (Quadratic)
- Number of Terms: [tex]\(3\)[/tex] (Trinomial)
Therefore, the polynomial [tex]\(-3x^2 + 3x + 5\)[/tex] is a Quadratic Trinomial.
### Conclusion
Considering all these factors, the correct classification of the polynomial [tex]\(7x - 3x^2 - 4x + 5\)[/tex] is:
[tex]\[ \boxed{\text{Quadratic Trinomial}} \][/tex]
So, the correct answer is:
C. Quadratic Trinomial
