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Which of the following expressions are polynomial in one variable and which are not? State reason for your answer.

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

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

3) $3 \sqrt{t} + t \sqrt{2}$

4) $y + \frac{2}{y}$

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

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First and second are polynomial in one variable

Third, fourth and fifth are polynomial in one variable

All

None

answer is A.

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Detailed Solution

(1) In

4 x^{2} - 3 x + 7

,Index of x is whole numbers. So, x is polynomial in one variable.
(2) In

y^{2} + \sqrt{2}

, Index of y is a whole number. So, y is polynomial in one variable.
(3) In

3 \sqrt{t} + t \sqrt{2} = 3 t^{\frac{1}{2}} + \sqrt{2} t

, Index of t is 1/2, which is not whole number. So,it is not a polynomial.
(4) In

y + \frac{2}{y} = y + 2 y^{- 1}

, here the exponent of first term is −1, which is not whole number. So, it is not a polynomial.
(5) In

x^{10} + y^{3} + t^{50}

is not a polynomial in one variable as three variable x, y and t occur in it.
Correct option is 1.

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