Question

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
ANSWERED
asked 2021-06-03
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.
\(g(x)=3-\frac{x^{2}}{4}\)

Answers (1)

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,
\(g(x)=a_{2}x^{2}+a_{1}x+a_{0},\ where\ a_{2}=-\frac{1}{4}, a_{1}=0\ and\ a_{0}=3\)
\(\Rightarrow g(x)=-\frac{1}{4}x^{2}+3\)

0
 
Best answer

expert advice

Need a better answer?

Relevant Questions

asked 2021-05-25
Determine whether the following function is a polynomial function. If the function is a polynomial​ function, state its degree. If not why? Write the polynomial in standard form. Then identify the leading term and the constant term.
\(G(x)=2(x-3)^{2}(x^{2}+5)\)
asked 2021-05-01
Determine whether \(g(x)=\frac{x^{3}}{2} -x^{2}+2\) 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.
asked 2021-06-04
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.
asked 2021-05-05
For each polynomial, state the constant term, the leading coefficient, and the degree of the polynomial.
\(5x^{2}-8x+2x^{4}-3\)
asked 2021-05-09
For each polynomial, state the constant term, the leading coefficient, and the degree of the polynomial.
\(5x^{2}-6x^{3}+3x^{6}+7\)
asked 2021-05-08
write the polynomial in descending order. Then identify the leading coefficient and degree of the polynomial.
\(\frac{y}{3}-y^{2}\)
asked 2021-02-03
Determine whether \(\displaystyle{g{{\left({x}\right)}}}={\frac{{{x}^{{3}}}}{{{2}}}}−{x}^{{2}}+{2}\) 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.
asked 2021-05-11
Consider the polynomial function \(p(x)=(3x^{2}-5x-2)(x-5)(x^{2}-4)\).
A) what is the degree of the polynomial? What is the y intercept of the function?
B)What are the zeros and their multiplicities?
C) what is the leading term of the polynomial and what power function has a graph most similiar to the graph of p?
asked 2021-06-07
For the following exercise, for each polynomial, a. find the degree; b. find the zeros, if any; c. find the y-intercept(s), if any; d. use the leading coefficient to determine the graph’s end behavior; and e. determine algebraically whether the polynomial is even, odd, or neither.
\(\displaystyle{f{{\left({x}\right)}}}={x}^{{3}}+{3}{x}^{{2}}-{x}-{3}\)
asked 2021-05-14
Determine whether each of the given sets is a real linear space, if addition and multiplication by real scalars are defined in the usual way. For those that are not, tell which axioms fail to hold. The function are real-valued. All rational functions f/g, with the degree off ≤≤ the degree ofg (including f = 0).
...