Question

Which of the following expressions is not a polynomial ?
a) 6x^2 - Root 6
b) x-1/x
c) 8x^2-1/2x+1
d) Root 2 * 4x^2 +1

Answer 1

Dear Student,
Here is the solution of your question.

(a). Given expression is $x^2-\sqrt{6}$ . This is a polynomial of degree two, because all the power of the variable $x$ are either a natural number or zero.

(b) Given expression is $x-\frac{1}{x}$.
This expression can be written as $x-x^{-1}$. Hence the given expression is not a polynomial because the variable $x$ has a power $-1$ involved in it.

(c) The given expression is $8x^2-\frac{1}{2x}+1$.
This expression can be written as $8x^2-\frac{1}{2}{x}^{-1}+1$. Hence the given expression is not a polynomial because the variable $x$ has a power $-1$ involved in it.

(d) The given expression is $\sqrt{2}\times 4x^2+1$. Hence given expression is a polynomial as all the power of the variable $x$ are non negative integer.

Regards
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