To determine the type of polynomial, we need to look at the highest power of [tex]\(x\)[/tex] present in the polynomial. Here's how you can do it step-by-step:
1. Identify the polynomial: The given polynomial is [tex]\(3x^3 - 5x^2 + 3x + 2\)[/tex].
2. Find the highest power of [tex]\(x\)[/tex]:
- The polynomial has four terms: [tex]\(3x^3\)[/tex], [tex]\(-5x^2\)[/tex], [tex]\(3x\)[/tex], and [tex]\(2\)[/tex].
- The powers of [tex]\(x\)[/tex] in these terms are [tex]\(3\)[/tex], [tex]\(2\)[/tex], [tex]\(1\)[/tex], and [tex]\(0\)[/tex], respectively.
3. Determine the highest power: Among these powers, the highest one is [tex]\(3\)[/tex].
4. Classify the polynomial by its degree:
- A polynomial is classified by its highest degree term.
- A polynomial with the highest degree of [tex]\(3\)[/tex] is called a cubic polynomial.
Therefore, the type of polynomial [tex]\(3x^3 - 5x^2 + 3x + 2\)[/tex] is cubic.
