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Standard X

Mathematics

Quadratic Equation as Product of 2 First Degree Equations

Which one of ...

Question

Which one of the following is a polynomial?

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

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\sqrt{2 x} - 1

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

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

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Solution

The correct option is D $x^{2} + \frac{3 x^{\frac{3}{2}}}{\sqrt{x}}$
The power of $x$ must be a non-negative integer in a polynomial.
Hence, option C is correct.
As we can write option c as
$x^{2} + 3 x^{\frac{3}{2} - \frac{1}{2}} = x^{2} + 3 x$

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Similar questions

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. Which of the following polynomials has (x + 1) as a factor?
I.

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

II.

x^{4} + x^{3} + x^{2} + x + 1

III.

x^{4} + 3 x^{3} + 3 x^{- 2} + x + 1

II.

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

Q. Determine which of the following polynomials has

(x + 1)

a factor:
(i)

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

(ii)

x^{4} + x^{3} + x^{2} + x + 1

(iii)

x^{4} + 3 x^{3} + 3 x^{2} + x + 1

(iv)

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

Q. Question 1
Determine which of the following polynomials has (x+1) a factor:
(i)

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

(ii)

x^{4} + x^{3} + x^{2} + x + 1

(iii)

x^{4} + 3 x^{3} + 3 x^{2} + x + 1

(iv)

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

Q. Question 1
Determine which of the following polynomials has (x+1) a factor:
(i)

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

(ii)

x^{4} + x^{3} + x^{2} + x + 1

(iii)

x^{4} + 3 x^{3} + 3 x^{2} + x + 1

(iv)

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

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Which one of the following is a polynomial?

The correct option is D x2+3x32√xThe power of x must be a non-negative integer in a polynomial.Hence, option C is correct.As we can write option c asx2+3x32−12=x2+3x

The correct option is D $x^{2} + \frac{3 x^{\frac{3}{2}}}{\sqrt{x}}$
The power of $x$ must be a non-negative integer in a polynomial.
Hence, option C is correct.
As we can write option c as
$x^{2} + 3 x^{\frac{3}{2} - \frac{1}{2}} = x^{2} + 3 x$