Answer :
Answer:
Only natural numbers (i.e., non-negative integers) can be the exponents of variables in a polynomial.
Step-by-step explanation:
The exponent of variables in a polynomial should be natural numbers ([tex]0[/tex], [tex]1[/tex], [tex]2[/tex], [tex]3[/tex], [tex]\dots[/tex].)
- [tex]\sqrt{2\, x}[/tex] is equal to [tex]\sqrt{2}\, x^{1/2}[/tex]. In this expression, [tex]x[/tex] is the variable. Its exponent is [tex]1/2[/tex], which isn't a natural number.
- On the other hand, [tex]\sqrt{2}\, x[/tex] is equivalent to [tex]\sqrt{2}\, x^{1}[/tex]. The exponent of variable [tex]x[/tex] is [tex]1[/tex], which is indeed a natural number.
[tex]\sqrt{2\, x}[/tex] isn't a polynomial because the exponent of variable [tex]x[/tex] isn't a natural number. On the other hand, [tex]\sqrt{2}\, x[/tex] is indeed a polynomial over the set of real numbers.