Which of the following is not a polynomial - a -3 x2-2-3 x-5 b 9x2-4x-2 c 3-2x3-6x2-1-2x-8 d x-3-x

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Polynomial

Which of the ...

Question

Which of the following is not a polynomial ?

(a) $\sqrt{3} x^{2} - 2 \sqrt{3} x + 5$ (b) $9 x^{2} - 4 x + \sqrt{2}$

(c) $\frac{3}{2} x^{3} + 6 x^{2} - \frac{1}{\sqrt{2}} x - 8$ (d) $x + \frac{3}{x}$

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\sqrt{3} x^{2} - 2 \sqrt{3} x + 5

9 x^{2} - 4 x + \sqrt{2}

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

x + \frac{3}{x}

f (x) = 2 x^{3} + 6 x^{2} + 4 x

g (x) = x^{2} + 3 x + 2

f (x)

g (x)

2 x + 3

\begin{matrix} {lim}_{x \to 1} \frac{x^{2} - 3 x + 2}{x^{2} - 4 x + 3} {lim}_{x \to 2} \frac{x^{3} + x^{2} - 12}{x^{3} - x^{2} - x - 2} {lim}_{x \to \sqrt{2}} \frac{x^{2} + x \sqrt{2} - 4}{x^{2} - 3 x \sqrt{2} + 4} {lim}_{x \to 3} \frac{x^{3} - 3 x^{2} - x + 3}{x^{3} - 6 x^{2} + 9 x} \end{matrix}

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

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