Which of the following expression is a polynomial

\frac{2}{3} x^{4} - 7 x + 15

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8 x^{2} - 3 x + 6 \sqrt{x} + 1

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5 x^{2} - \frac{2}{x} + 7

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x^{2} + y^{2} + x y + x^{2} y^{2}

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Solution

The correct option is A $\frac{2}{3} x^{4} - 7 x + 15$
Clearly, only A is a polynomial, because a polynomial is a single variable equation and does not contain fractional or irrational term in variable x.

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Similar questions

Which of the following expressions is a polynomial ?
(a) $\sqrt{x} - 1$
(b) $\frac{x - 1}{x + 1}$
(c) $x^{2} - \frac{2}{x^{2}} + 5$
(d) $x^{2} + \frac{2 x^{\frac{3}{2}}}{\sqrt{x}} + 6$

Which of the following expressions are polynomials? In case of a polynomial, write its degree.

(i) $x^{5} - 2 x^{3} + x + \sqrt{3}$

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

(iii) $t^{2} - \frac{2}{5} t + \sqrt{5}$

(iv) $x^{1000} - 1$

(v) $\frac{1}{\sqrt{2}} x^{2} - \sqrt{2} x + 2$

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

(vii) $1$

(viii) $\frac{- 3}{5}$

(ix) $\frac{x^{2}}{2} - \frac{2}{x^{2}}$

(x) $\sqrt[2]{2} x^{2} - 8$

(xi) $\frac{1}{2 x^{2}}$

(xii) $\frac{1}{\sqrt{5}} x^{\frac{1}{2}} + 1$

(xiii) $\frac{3}{5} x^{2} - \frac{7}{3} x + 9$

(xiv) $x^{4} - x^{\frac{3}{2}} + x - 3$

(xv) $2 x^{3} + 3 x^{2} + \sqrt{x} - 1$

Find the value of each given polynomial at the given value of its variable :
(i) $5 x^{2} - 7 x + 2$ at x = 2
(ii) $x^{2} + 15 x - 4$ at x = -3
(iii) $3 y + 8 - 2 y^{2}$ at y = –3
(v) $x^{2} + 3 x + 1$ at x = -1/3
(v) $x^{3} - 3 x^{2} + 5 x + 2$ at x = – 1