Choose the correct classification of 3x⁴ - 9x³ - 3x² + 6.
5th degree polynomial
4th degree polynomial
9th degree polynomial
24th degree polynomial

Solution:

The correct classification of the polynomial 3x⁴ - 9x³ - 3x² + 6 is that it is a 4th degree polynomial.

The reason is that the highest power of x is 4 and hence it is 4th degree.

It is a polynomial because it has more than one term which include lower powers of x i.e. - 9x³ , - 3x² , and 6x⁰.

The degree of the polynomial is decided by the highest power of the variable it carries. In the given problem the highest power of x is four.

Let us take another example in which each term has more than one variable as shown below: 6x²y + 8x² - 30y - 40

In this case the degree of the polynomial is 3 which is obtained by adding the powers of x and y in

The first term i.e. 6x²y which 2 + 1 = 3.

Choose the correct classification of 3x⁴ - 9x³ - 3x² + 6.

Summary:

The correct classification of the polynomial 3x⁴ - 9x³ - 3x² + 6 is that it is a 4th degree polynomial.