Question

What is the degree of the polynomial $\frac{7x^2+2x^5+4x}{3x}?$

• A. $2$
• B. $3$
• C. $4$
• D. $5$

Answer 1

The correct option is C $4$

$\underset{–}{\text{Need to Find:}}$
Degree of the polynomial $\frac{7x^2+2x^5+4x}{3x}$

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

$\frac{7x^2+2x^5+4x}{3x}$ can be written as

$\to \frac{7x^2}{3x}+\frac{2x^5}{3x}+\frac{4x}{3x}$

$\to \frac{7}{3}{x}^{(2-1)}+\frac{2}{3}{x}^{(5-1)}+\frac{4}{3}{x}^{(1-1)}$ $[\because \frac{a^m}{a^n}=a^{(m-n)}]$

$\to \frac{7}{3}x+\frac{2}{3}{x}^4+\frac{4}{3}{x}^0$
Arranging the terms in descending order of their powers

$=\frac{2}{3}{x}^4+\frac{7}{3}x+\frac{4}{3}$ $[\because x^0=1]$

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 $\underset{–}{4}.$ Therefore, degree of the given polynomial is $\underset{–}{4}.$

Hence, option (c.) is the correct choice.