# Determine whether the following function is a polynomial function. If the function is a polynomial​ function, state its degree. If it is​ not, tell why not. Write the polynomial in standard form. Then identify the leading term and the constant term. g(x)=3-\frac{x^{2}}{4}

Polynomial factorization
Determine whether the following function is a polynomial function. If the function is a polynomial​ function, state its degree. If it is​ not, tell why not. Write the polynomial in standard form. Then identify the leading term and the constant term.
$$g(x)=3-\frac{x^{2}}{4}$$

2021-06-04

Step 1
The given function is,
$$g(x)=3-\frac{x^{2}}{4}\ or\ g(x)=-\frac{1}{4}x^{2}+3$$.
From the definition of polynomial function, it can be said that, the given function is a polynomial function.
The highest power of x in the expression $$3-\frac{x^{2}}{4}$$ is 2.
Thus, degree of the polynomial is 2.
Step 2
The standard form of a polynomial function is,
$$g(x)=a_{2}x^{2}+a_{1}x+a_{0},\ where\ a_{2}=-\frac{1}{4}, a_{1}=0\ and\ a_{0}=3$$
$$\Rightarrow g(x)=-\frac{1}{4}x^{2}+3$$