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Standard IX

Mathematics

Polynomial Expressions

Which of the ...

Question

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

(i) (ii) (iii)

(iv) (v)

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Solution

(i)

Yes, this expression is a polynomial in one variable x.

(ii)

Yes, this expression is a polynomial in one variable y.

(iii)

No. It can be observed that the exponent of variable t in term is , which is not a whole number. Therefore, this expression is not a polynomial.

(iv)

No. It can be observed that the exponent of variable y in termis −1, which is not a whole number. Therefore, this expression is not a polynomial.

(v)

No. It can be observed that this expression is a polynomial in 3 variables x, y, and t. Therefore, it is not a polynomial in one variable.

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Similar questions

Q. Question 1
Which of the following expressions are polynomials in one variable and which are not?
(i)

4 x^{2} - 3 x + 7

(ii)

y^{2} + \sqrt{2}

(iii)

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

(iv)

y + \frac{2}{y}

(v)

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

Q. Question 1
Which of the following expressions are polynomials in one variable and which are not?
(i)

4 x^{2} - 3 x + 7

(ii)

y^{2} + \sqrt{2}

(iii)

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

(iv)

y + \frac{2}{y}

(v)

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

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

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

(i i) y^{2}

\sqrt{2}

(i i i) 3 \sqrt{t} + t \sqrt{2}

Which of the following expression are polynomials in one variable and which not ? State reason for your answe.
$(i) 4 x^{2} - 3 x + 7$
$(i i) y^{2} + \sqrt{2}$

$(i i i) 3 \sqrt{1} + 1 \sqrt{2}$

$(i v) y + \frac{2}{y}$

Q. Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer:

(i) 3x² − 4x + 15

(ii) y² + 2

\sqrt{3}

(iii)

3 \sqrt{x} + \sqrt{2} x

(iv)

x - \frac{4}{x}

(v) x¹² + y³ + t⁵⁰

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Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer. (i) (ii) (iii) (iv) (v)

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

(i) (ii) (iii)

(iv) (v)