Question

If the given expression is a polynomial, find its degree.
$4y+7+\frac{x^{5/2}y}{x^{1/2}}+2x^2$

• A. The expression is not a polynomial and hence does not have a degree.
• B. 0
• C. 2
• D. 3

Answer 1

The correct option is D 3

$4y+7+\frac{x^{5/2}y}{x^{1/2}}+2x^2$

Simplifying the third term by adding/subtracting the exponents of same variables we get,

$\frac{x^{5/2}y}{x^{1/2}}=x^{(5/2-1/2)}y=x^{4/2}y=x^{2}y$

$\therefore$ The original expression becomes

$\Rightarrow 4y+7+x^{2}y+2x^2$

As the exponents of all the variables are the whole number this is a polynomial and has a valid degree.

Identifying the degree of each monomial,

1. $4y=4y^1\to \text{Degree}=1$
2. $7=7x^0\to \text{Degree}=0$
3. $x^{2}y=x^2{y}^1\to \text{Degree}=2+1=3$
4. $2x^2\to \text{Degree}=2$

The degree of the polynomial is given by the maximum degree of each monomial of the polynomial.

Here the largest degree is 3. Hence, the degree of the polynomial is 3.