Question

What is the degree of the expression $2x^{\frac{5}{2}}\cdot 3x^{\frac{5}{2}}-6x^5?$

• A. $0$
• B. $1$
• C. $5$
• D. Not defined

Answer 1

The correct option is D Not defined

$\underset{–}{\text{Need to Find:}}$ Degree of the expression $2x^{\frac{5}{2}}\cdot 3x^{\frac{5}{2}}-6x^5$

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

$2x^{\frac{5}{2}}\cdot 3x^{\frac{5}{2}}-6x^5$

$=2\cdot 3\cdot x^{\frac{5}{2}}\cdot x^{\frac{5}{2}}-6x^5$

$=6\cdot x^{(\frac{5+5}{2})}-6x^5[\because a^m\cdot a^n=a^{(m+n)}]$

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

$=6\cdot x^{(\frac{10}{2})}-6x^5$

$=6\cdot x^{(\frac{5\times 2}{2})}-6x^5$

$=6\cdot x^5-6x^5$

$=0$

As a result, given expression is simplified to a $\underset{–}{\text{zero polynomial}}.$ And as we know, degree of a $\underset{–}{\text{zero polynomial}}$ is $\underset{–}{\text{not defined}}.$ Therefore, degree of the given expression is $\underset{–}{\text{not defined}}.$

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