Question

The degree of the expression $\dfrac{5x^3+2}{3x^{-2}$ is

Answer 1

$\underset{–}{\text{Need to Find:}}$
Degree of the expression: $\frac{5x^3+2}{{3x}^{-2}}$

As the given polynomial is not in standard form, we'll simplify it and express it in standard form first.

$\frac{5x^3+2}{{3x}^{-2}}$

$=\frac{5x^3}{3x^{-2}}+\frac{2}{3x^{-2}}$

$=\frac{5}{3}{x}^{3-(-2)}+\frac{2}{3}{x}^{0-(-2)}$ $[\because \frac{a^m}{a^n}=a^{m-n}]$

$=\frac{5}{3}{x}^5+\frac{2}{3}{x}^2$

Now, as we know, the largest power of the variable is the degree of the polynomial. Here, the largest power of the variable $\underset{–}{x}$ is $\underset{–}{5}.$ Therefore, degree of the given polynomial is $\underset{–}{5}.$