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Standard IX

Mathematics

Polynomials

Which of the ...

Question

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

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

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

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

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Solution

(i) $\frac{x^{2}}{2} - \frac{2}{x^{2}}$ . This is an expression having a negative integral power of x i.e. −2. So, it is not a polynomial.

(ii) $\sqrt[2]{2} x^{2} - 8$ is an expression having an only non-negative integral power of x. So, it is a polynomial. Also, the highest power of x is 2, so, it is a polynomial of degree 2.

(iii) $\frac{1}{2 x^{2}}$ is an expression having a negative integral power of x. So, it is not a polynomial.

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

Q. The expression

{(\sqrt{2 x^{2} + 1} + \sqrt{2 x^{2} - 1})}^{6}

{(\frac{2}{\sqrt{2 x^{2} + 1} + \sqrt{2 x^{2} - 1}})}^{6}

is a polynomial of degree

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

Q. 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^{100} - 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[3]{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

Q. The expression

(\sqrt{2 x^{2} + 1} + \sqrt{2 x^{2} - 1})^{6} + {(\frac{2}{\sqrt{2 x^{2} + 1} + \sqrt{2 x^{2} - 1}})}^{6}

is a polynomial of degree

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Which of the following expressions are polynomials? In case of a polynomial, write its degree. (i) x22−2x2 (ii) 2√2x2−8 (iii) 12x2

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

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

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

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