Question

What is the degree of the polynomial $2x+\frac{7x^{\frac{9}{2}}}{x^{\frac{3}{2}}}+5?$

• A. $3$
• B. $2$
• C. $1$
• D. $0$

Answer 1

The correct option is A $3$

$\underset{–}{\text{Need to Find:}}$
Degree of the polynomial, $2x+\frac{7x^{\frac{9}{2}}}{x^{\frac{3}{2}}}+5$

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

$2x+\frac{7x^{\frac{9}{2}}}{x^{\frac{3}{2}}}+5$

$=2x+7x^{(\frac{9}{2}-\frac{3}{2})}+5$ $[\because \frac{a^m}{a^n}=a^{(m-n)}]$

$=2x+7x^{(\frac{9-3}{2})}+5$

$=2x+7x^{(\frac{6}{2})}+5$

$=2x+7x^{(\frac{3\times 2}{2})}+5$

$=2x+7x^3+5$
Arranging the terms in descending order of their powers

$=7x^3+2x+5$

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 $\underset{–}{3}.$ Therefore, degree of the given polynomial is $\underset{–}{3}.$

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