Which of the following expressions is a polynomial in one variable- a x-2-x-3 b 3-x-2-x-5 c -2x2-3x-6 d x10-y5-8

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Standard IX

Mathematics

Types of Polynomials

Which of the ...

Question

Which of the following expressions is a polynomial in one variable?
(a) $x + \frac{2}{x} + 3$
(b) $3 \sqrt{x} + \frac{2}{\sqrt{x}} + 5$
(c) $\sqrt{2} x^{2} - \sqrt{3} x + 6$
(d) $x^{10} + y^{5} + 8$

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Solution

(c) $\sqrt{2} x^{2} - \sqrt{3} x + 6$

Clearly, $\sqrt{2} x^{2} - \sqrt{3} x + 6$ is a polynomial in one variable because it has only non-negative integral powers of x.

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Similar questions

Q. Which of the following expressions is a polynomial in one variable?
(a)

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

(b)

3 \sqrt{x} + \frac{2}{\sqrt{x}} + 5

(c)

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

(d) x¹⁰ + y⁵ + 8

A polynomial
$P (x) = x^{2} + 2 x + 3$
leaves a remainder of ___ when divided by $x - 1$ .

Which of the following is a polynomial ?

(a) $x^{2} - 5 x + 4 \sqrt{x} + 3$ (b) $x^{\frac{3}{2}} - x + x^{\frac{1}{2}} + 1$

Which of the following is not a quadratic equation?
(a) $3 x - x^{2} = x^{2} + 5$
(b) $(x + 2)^{2} = 2 (x^{2} - 5)$
(c) $(2 x + 3)^{2} = 2 x^{2} + 6$
(d) $(x - 1)^{2} = 3 x^{2} + x - 2$

Q. Mark (✓) against the correct answer in each of the following:
Which of the following is a polynomial in one variable?
(a) x² + x⁻²
(b)

\sqrt{3 x} + 9

(c)

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

(d)

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

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Which of the following expressions is a polynomial in one variable? (a) x+2x+3 (b) 3√x+2√x+5 (c) √2x2−√3x+6 (d) x10+y5+8

(c) √2x2−√3x+6 Clearly, √2x2−√3x+6 is a polynomial in one variable because it has only non-negative integral powers of x.

Which of the following expressions is a polynomial in one variable?
(a) $x + \frac{2}{x} + 3$
(b) $3 \sqrt{x} + \frac{2}{\sqrt{x}} + 5$
(c) $\sqrt{2} x^{2} - \sqrt{3} x + 6$
(d) $x^{10} + y^{5} + 8$

(c) $\sqrt{2} x^{2} - \sqrt{3} x + 6$

Clearly, $\sqrt{2} x^{2} - \sqrt{3} x + 6$ is a polynomial in one variable because it has only non-negative integral powers of x.