Question:
Which of the following expressions is a polynomial in one variable?
(a) $x+\frac{2}{x}+3$
(b) $3 \sqrt{x}+\frac{2}{\sqrt{x}}+5$
(c) $\sqrt{2} x^{2}-\sqrt{3} x+6$
(d) $x^{10}+y^{5}+8$
Solution:
(c) $\sqrt{2} x^{2}-\sqrt{3} x+6$
Clearly, $\sqrt{2} x^{2}-\sqrt{3} x+6$ is a polynomial in one variable because it has only non-negative integral powers of $x$.
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