Certainly! Let's analyze the polynomial [tex]\(3x^3 - 5x^2 + 3x + 2\)[/tex] step-by-step.
1. Identify the Polynomial:
The given expression is [tex]\(3x^3 - 5x^2 + 3x + 2\)[/tex].
2. Break Down the Polynomial:
- The term [tex]\(3x^3\)[/tex] has a degree of 3.
- The term [tex]\(-5x^2\)[/tex] has a degree of 2.
- The term [tex]\(3x\)[/tex] has a degree of 1.
- The constant term [tex]\(2\)[/tex] has a degree of 0.
3. Determine the Degree of the Polynomial:
The degree of a polynomial is determined by the highest power of the variable [tex]\(x\)[/tex] in the polynomial. Here, the highest power of [tex]\(x\)[/tex] is 3, which comes from the term [tex]\(3x^3\)[/tex].
4. Classify the Polynomial:
Polynomials are classified based on their degree:
- A polynomial of degree 1 is called a linear polynomial.
- A polynomial of degree 2 is called a quadratic polynomial.
- A polynomial of degree 3 is called a cubic polynomial.
- And so forth.
Since the highest power of [tex]\(x\)[/tex] in the polynomial [tex]\(3x^3 - 5x^2 + 3x + 2\)[/tex] is 3, this makes it a polynomial of degree 3.
5. Conclusion:
A polynomial of degree 3 is known as a cubic polynomial.
Therefore, the given polynomial [tex]\(3x^3 - 5x^2 + 3x + 2\)[/tex] is a cubic polynomial.
