Question

Identify which of the following algebraic expressions are polynomials. If so, write their degrees.

$x^3+\frac{1}{3x^2}+7$

Answer 1

Given algebraic expression is $x^3+\frac{1}{3x^2}+7$

An algebraic expression is said to be a polynomial if the power of its variable is either zero or positive in all terms.

Here, the algebraic expression $x^3+\frac{1}{3x^2}+7$ is the variable of $x$

So, the power of $x$in the term $x^3=3$

the power of $x$in the term $\frac{1}{3x^2}=-2$

the power of $x$in the term $7=0$

Since, the power of $x$ in the term $\frac{1}{3x^2}$is $-2$which is negative.

Hence, it is not a polynomial.