Step 1

Given function is,

\(F(x)=5x^{4}-\pi x^{3}+\frac{1}{2}\)

The objective is to determine whether F(x) is a polynomial or not. If yes then state its degree, if not then given the reason why it is not a polynomial.

Step 2

Yes, F(x) is a polynomial of degree 4 with leading coefficient 5 and constant term \(\frac{1}{2}\).

Standard form: \(F(x)=5x^{4}-\pi x^{3}+0x^{2}+0x+\frac{1}{2}\)

Given function is,

\(F(x)=5x^{4}-\pi x^{3}+\frac{1}{2}\)

The objective is to determine whether F(x) is a polynomial or not. If yes then state its degree, if not then given the reason why it is not a polynomial.

Step 2

Yes, F(x) is a polynomial of degree 4 with leading coefficient 5 and constant term \(\frac{1}{2}\).

Standard form: \(F(x)=5x^{4}-\pi x^{3}+0x^{2}+0x+\frac{1}{2}\)