Which of the following is a polynomial of degree 2?

2 x^{2} - 2 x^{1.5} + 1

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

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(x^{2} + x + 2) x

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

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Solution

The correct option is D $2 x^{3} + 3 x^{2} - 2 x^{3} + 1$
$(2 x^{2} - 2 x^{1.5} + 1)$ is not a polynomial since it contains a term in which the variable has fractional exponent.
$(3 x^{2} + x - x^{2} + 2 - 2 x^{2}) = (x + 2)$ is a polynomial of degree 1,
$(x^{2} + x + 2) x = (x^{3} + x^{2} + 2 x)$ is a polynomial of degree 3.
$(2 x^{3} + 3 x^{2} - 2 x^{3} + 1) = (3 x^{2} + 1)$ is a polynomial of degree 2.

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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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