To classify the polynomial [tex]\(3x^4 - 9x^3 - 3x^2 + 6\)[/tex], we need to determine its degree. The degree of a polynomial is the highest power of the variable [tex]\(x\)[/tex] that appears in the polynomial with a non-zero coefficient. Let's examine the terms of the polynomial:
- The first term is [tex]\(3x^4\)[/tex] with a degree of 4.
- The second term is [tex]\(-9x^3\)[/tex] with a degree of 3.
- The third term is [tex]\(-3x^2\)[/tex] with a degree of 2.
- The constant term [tex]\(6\)[/tex] has a degree of 0 (since it can be considered as [tex]\(6x^0\)[/tex]).
Among these terms, the highest degree is 4, which comes from the term [tex]\(3x^4\)[/tex].
Therefore, the polynomial [tex]\(3x^4 - 9x^3 - 3x^2 + 6\)[/tex] is a 4th degree polynomial.
The correct classification is:
4th degree polynomial
