Are the following expressions polynomials? Justify your answer:
$\frac{1}{7} a^{3}-\frac{2}{\sqrt{3}} a^{2}+4 a-7$
$\frac{1}{7} a^{3}-\frac{2}{\sqrt{3}} a^{2}+4 a-7$
(A) The given expression is $\frac{1}{7} a^{3}-\frac{2}{\sqrt{3}} a^{2}+4 a-7$.
$A$ polynomial is an algebraic expression in which the exponents of the variables are non-negative integers (whole numbers).
In the given expression,the exponents of the variable $a$ are $3$,$2$,and $1$ (for the term $4a$),and the constant term $-7$ can be written as $-7a^0$.
Since all exponents $(3, 2, 1, 0)$ are whole numbers,the expression is a polynomial.
$A$ polynomial is an algebraic expression in which the exponents of the variables are non-negative integers (whole numbers).
In the given expression,the exponents of the variable $a$ are $3$,$2$,and $1$ (for the term $4a$),and the constant term $-7$ can be written as $-7a^0$.
Since all exponents $(3, 2, 1, 0)$ are whole numbers,the expression is a polynomial.
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