Which of the following expression is a polynomial-a x-1b x-1 x-1c x 2-2 - 2-5d x 2-2 x 3 - 2 x-6

(d) x2+2x3/2x+6 We have: x2+2x32x+6=x2+2x32x 12+6 nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; =x2+2x+6 nbsp; It a polynomial bec ...

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Byju's Answer

Standard IX

Mathematics

Polynomials

Which of the ...

Question

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

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Solution

(d) $x^{2} + \frac{2 x^{3 / 2}}{\sqrt{x}} + 6$

We have:

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

It a polynomial because it has only non-negative integral powers of 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) $x^{2} + \frac{2 x^{\frac{3}{2}}}{\sqrt{x}} + 6$

Q. Which one of the following is a polynomial?

(a)

\frac{x^{2}}{2} - \frac{2}{x^{2}}

(b)

\sqrt{2 x} - 1

(c)

x^{2} + \frac{3 x^{3 / 2}}{\sqrt{x}}

(4)

\frac{x - 1}{x + 1}

Q. Which of the following is a polynomial?

(a)

x^{2} - 5 x + 4 \sqrt{x} + 3

(b)

x^{3 / 2} - x + x^{1 / 2} + 1

(c)

\sqrt{x} + \frac{1}{\sqrt{x}}

(d)

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

Question 1
Which one of the following is a polynomial?

A) $\frac{x^{2}}{2} - \frac{2}{x^{2}}$
B) $\sqrt{2 x} - 1$
C) $x^{2} + \frac{3 x^{\frac{3}{2}}}{\sqrt{x}}$
D) $\frac{x - 1}{x + 1}$

Q. The factors of x³ − 7x + 6 are

(a) x (x − 6) (x − 1)

(b) (x² − 6) (x − 1)

(c) (x + 1) (x + 2) (x + 3)

(d) (x − 1) (x + 3) (x − 2)

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Which of the following expression is a polynomial? (a) x-1 (b) x-1x+1 (c) x2-2x2+5 (d) x2+2x3/2x+6

(d) x2+2x3/2x+6 We have: x2+2x32x+6=x2+2x32x-12+6 =x2+2x+6 It a polynomial because it has only non-negative integral powers of x.

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

(d) $x^{2} + \frac{2 x^{3 / 2}}{\sqrt{x}} + 6$

We have:

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

It a polynomial because it has only non-negative integral powers of x.