Question

Is \(9 x^{2}+8 x-4 x^{3}+3\) a polynomial with a degree of \(2 ?\) Explain.

Short answer

No, \(9 x^{2}+8 x-4 x^{3}+3\) is not a polynomial of degree 2; it is a polynomial of degree 3.

Step-by-step solution

Understanding a Polynomial

A polynomial is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. In the case of a single variable, the degree of the polynomial is the highest power of that variable in any term.

Identify the Highest Power

Looking at \(9 x^{2}+8 x-4 x^{3}+3\), there are terms with powers of 2 and 3 on the variable x. Therefore, the highest power is 3, given by the term \(-4x^3\).

Conclusion

Since the highest power of the variable x in the given expression is 3, the degree of the polynomial \(9 x^{2}+8 x-4 x^{3}+3\) is 3, not 2.