Which of the following expressions is a polynomial in one variable?

$x^{π} + x^{- 2}$

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$π x^{3} + 3 x^{2} + 9$

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$2 x^{4} + 4 x^{3 / 2} + 2$

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$3 x^{2} + 4 x y + \sqrt{2}$

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Solution

The correct option is B
$π x^{3} + 3 x^{2} + 9$

i) $x^{π} + x^{- 2}$ is not a polynomial because the exponents $π$ and -2 are not whole numbers.
ii) $π x^{3} + 3 x^{2} + 9$ is a polynomial as each exponent is a whole number.
iii) $2 x^{4} + 4 x^{3 / 2} + 2$ is not a polynomial as one of the exponents, $\frac{3}{2}$ , is not a whole number.
iv) $3 x^{2} + 4 x y + \sqrt{2}$ is a polynomial in two variables, x and y.

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Similar questions

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) $x^{10} + y^{5} + 8$

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

Assertion: The expression $3 x^{4} - 4 x^{\frac{3}{2}} + x^{2}$ is not a polynomial because the term $- 4 x^{\frac{3}{2}}$ contains a rational power of x.

Reason: The highest exponent(of the variable) in various terms of a polynomial in one variable is called its degree.

Which of the following is true?

Q. Is the given expression a polynomial?

\frac{3}{7} x^{2} + 4 x y + 2 y^{2}

Statement1: The polynomial $P (x) = 4 x^{3} - 3 x^{2} + 5 x - 6$ when divided by $x - 1$ gives zero as the remainder.

Statement2: $(x - 1)$ is a factor of the polynomial $P (x) = 4 x^{3} - 3 x^{2} + 5 x - 6$ .

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