Question

Which among the following is not a polynomial?

• A. $5b$
• B. $10x+6y+8z$
• C. $9c-14d$
• D. $\frac{3}{p}+7q$
  

Answer 1

The correct option is D $\frac{3}{p}+7q$


In a polynomial, the power of variable of each term should be a $\underset{–}{\text{whole number}}$.

The term $\underset{–}{16x^y}$ of a polynomial has components as shown in below picture,


$\bullet$ (a.) $\underset{–}{5b:}$
In option (a.), the term given is $5b$. Here the power of variable '$b$' is $1$, i.e., a whole number and hence, it is a polynomial.

$\bullet$ (b.) $\underset{–}{10x+6y+8z:}$
In option (b.), the expression given is $10x+6y+8z$. Here the power of each of the variables '$x$', '$y$' and '$z$' is $1$, i.e., a whole number, and so it is a polynomial.

$\bullet$ (c.) $\underset{–}{9c-14d:}$
In option (c.), the expression given is $9c-14d$. Here the power of each of the variables '$c$' and '$d$' is $1$, i.e., a whole number, and so it is a polynomial.

$\bullet$ (d.) $\underset{–}{\frac{3}{p}+7q=3p^{-1}+7q}$

$[\because \frac{1}{a^n}=a^{-n}]$

In option (d.), the expression given is $\frac{3}{p}+7q$. Here the power of one variable '$p$' is $-1$, i.e., not a whole number and the power of another variable '$q$' is $1$, i.e., a whole number but for a polynomial the power of variable in each term must be a whole number and hence, $\frac{3}{p}+7q$ is not a polynomial.


Therefore, option (d.) is the correct answer.