Question

Write all the terms of the following algebraic expressions and identify the polynomial.

$\mathrm{x}+\mathrm{y}+{\mathrm{xy}}^2+\frac{2}{5}{\mathrm{y}}^3+\frac{3}{4}{\mathrm{y}}^5$

Answer 1

Step 1: Writing the terms of algebraic expressions

The given expression is $\mathrm{x}+\mathrm{y}+{\mathrm{xy}}^2+\frac{2}{5}{\mathrm{y}}^3+\frac{3}{4}{\mathrm{y}}^5$

The terms are $\mathrm{x},\mathrm{y},\mathrm{z},{\mathrm{xy}}^2,\frac{2}{5}{\mathrm{y}}^3\mathrm{and}\frac{3}{4}{\mathrm{y}}^5$

Step 2: Checking whether the expression is polynomial or not

We know that, a polynomial is a mathematic expression containing several terms where the variables have positive integral exponents.

Here, each term has a positive integral exponent.

Hence, $\mathrm{x}+\mathrm{y}+{\mathrm{xy}}^2+\frac{2}{5}{\mathrm{y}}^3+\frac{3}{4}{\mathrm{y}}^5$ is a polynomial.