Question:
Which of the following expression is a polynomial?
(a) $\sqrt{x}-1$
(b) $\frac{x-1}{x+1}$\
(c) $x^{2}-\frac{2}{x^{2}}+5$
(d) $x^{2}+\frac{2 x^{3 / 2}}{\sqrt{x}}+6$
Solution:
(d) $x^{2}+\frac{2 x^{3 / 2}}{\sqrt{x}}+6$
We have:
$x^{2}+\frac{2 x^{\frac{3}{2}}}{\sqrt{x}}+6=x^{2}+2 x^{\frac{3}{2}} x^{-\frac{1}{2}}+6$
$=x^{2}+2 x+6$
It a polynomial because it has only non-negative integral powers of x.
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