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Polynomials

Identify whet...

Question

Identify whether the given expressions are polynomials in one variable or not?
(i) $y + \frac{2}{y}$
(ii) $x^{10} + y^{3} + t^{50}$

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Solution

(i) $y + \frac{2}{y}$ is not a polynomial as power of y in second term, i.e., $\frac{1}{y} = y^{- 1}$ is not a whole number.

(ii) $x^{10} + y^{3} + t^{50}$ is not a polynomial in one variable but a polynomial in three variables x, y and t.

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Which of the following expressions are polynomials in one variable?

(1) $4 x^{2} - 3 x + 7$

(2) $y^{2} + \sqrt{2}$

(3) $y + \frac{2}{y}$

(4) $x^{10} + y^{3} + t^{50}$

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