Question

# Is the algebraic expression a polynomial? If it is, write the polynomial in standard form: 2x+3x^{2}-5

Applications of integrals
Is the algebraic expression a polynomial? If it is, write the polynomial in standard form:
$$\displaystyle{2}{x}+{3}{x}^{{{2}}}-{5}$$

2021-04-22
Step 1
A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using the mathematical operations such as addition, subtraction, multiplication and division.
A polynomial function is an expression constructed with one or more terms of variables with constant exponents. If there are real numbers denoted by a, then function with one variable and of degree n can be written as:
$$\displaystyle{f{{\left({x}\right)}}}={a}_{{{0}}}{x}^{{{n}}}+{a}_{{{1}}}{x}^{{{n}-{1}}}+{a}_{{{2}}}{x}^{{{n}-{2}}}+\ldots..+{a}_{{{n}-{2}}}{x}^{{{2}}}+{a}_{{{n}-{1}}}{x}+{a}_{{{n}}}$$
Given expression is
$$\displaystyle{2}{x}+{3}{x}^{{{2}}}-{5}$$.
Step 2
This can be in the form of algebraic expression of a polynomial that is:
$$\displaystyle{f{{\left({x}\right)}}}={3}{x}^{{{2}}}+{2}{x}-{5}$$
Also,
it is written in the standard form of polynomial i.e,
$$\displaystyle{f{{\left({x}\right)}}}={3}{x}^{{{2}}}+{2}{x}-{5}$$
It means decreasing power of x is there
standard form $$\displaystyle={3}{x}^{{{2}}}+{2}{x}-{5}$$