# Determine whether F(x)=5x^{4}-\pi x^{3}+\frac{1}{2} is a polynomial. If it is, state its degree. If not, say why it is not a polynomial. If it is a polynomial, write it in standard form. Identify the leading term and the constant term.

Polynomial factorization
Determine whether $$F(x)=5x^{4}-\pi x^{3}+\frac{1}{2}$$ is a polynomial. If it is, state its degree. If not, say why it is not a polynomial. If it is a polynomial, write it in standard form. Identify the leading term and the constant term.

2021-06-05
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: $$F(x)=5x^{4}-\pi x^{3}+0x^{2}+0x+\frac{1}{2}$$