Step 1

Expression given −

\(\displaystyle{x}^{{{2}}}-{x}^{{{3}}}+{x}^{{{4}}}-{5}\)

Any equation of the form of \(\displaystyle{a}_{{{n}}}{x}^{{{n}}}\) is a polynomial, where a is the coefficient and x is the variable.

So, the given expression is a polynomial.

Step 2

The standard form of a polynomial is the one in which the highest degree comes first and then the lower ones.

Standard form of given expression −

\(\displaystyle{x}^{{{4}}}-{x}^{{{3}}}+{x}^{{{2}}}-{5}\)

Expression given −

\(\displaystyle{x}^{{{2}}}-{x}^{{{3}}}+{x}^{{{4}}}-{5}\)

Any equation of the form of \(\displaystyle{a}_{{{n}}}{x}^{{{n}}}\) is a polynomial, where a is the coefficient and x is the variable.

So, the given expression is a polynomial.

Step 2

The standard form of a polynomial is the one in which the highest degree comes first and then the lower ones.

Standard form of given expression −

\(\displaystyle{x}^{{{4}}}-{x}^{{{3}}}+{x}^{{{2}}}-{5}\)