Which of the following expressions are polynomials in one variable and which are not?State reasons for your answer.
$(i) 4 x^{2} + 5 x - 2$
$(i i) y^{2}$
$(i i i) 5$
$(i v) 2 x^{2} + \frac{3}{x} - 5$

Open in App

Solution

$(i) 4 x^{2} + 5 x - 2$
$= 4 x^{2} + 5 x^{1} - 2 x^{0}$
Here power of expression is $2, 1, 0$
Since all powers are whole number, it is a polynomial.

$(i i) y^{2}$
Here the power of expression is $2$
Since power is a whole number, it is a polynomial.

$(i i i) 5 = 5 x^{0}$
Here power is $0$
Since power is a whole number, it is a polynomial.

$(i v) 2 x^{2} + \frac{3}{x} - 5$
$= 2 x^{2} + 3 x^{- 1} - 5 x^{0}$
Here power of expression is $2, - 1, 0$ where $- 1$ is not a whole number.
Hence it is not a polynomial

Suggest Corrections

Similar questions

(i) 4 x^{2} + 5 x - 2

(i i) y^{2}

(i i i) 5

(i v) 2 x^{2} + \frac{3}{x} - 5

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

(i i) y^{2}

\sqrt{2}

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

\sqrt{3}

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

x - \frac{4}{x}

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

(i) $3 x^{2} - 4 x + 15$

(ii) $y^{2} + 2 \sqrt{3}$

(iii) $3 \sqrt{x} + \sqrt{2} x$

(iv) $x - \frac{4}{x}$

(v) $x^{12} + y^{3} + t^{50}$

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

(i) (ii) (iii)

(iv) (v)

Join BYJU'S Learning Program