Which of the following is a polynomial of degree 2-2x-2 - 2x-1-5 - 13x-2 - x - x-2 - 2 - 2x-2-x-2 - x - 2-x nbsp-2x-3 - 3x-2 - 2x-3 - 1

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Standard X

Mathematics

Linear Polynomial and Its Graphical Representation

Which of the ...

Question

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

Which of the following expressions are polynomials? In case of a polynomial, write its degree.

(i) $x^{5} - 2 x^{3} + x + \sqrt{3}$

(ii) $y^{3} + \sqrt{3} y$

(iii) $t^{2} - \frac{2}{5} t + \sqrt{5}$

(iv) $x^{1000} - 1$

(v) $\frac{1}{\sqrt{2}} x^{2} - \sqrt{2} x + 2$

(vi) $x^{- 2} + 2 x^{- 1} + 3$

(vii) $1$

(viii) $\frac{- 3}{5}$

(ix) $\frac{x^{2}}{2} - \frac{2}{x^{2}}$

(x) $\sqrt[2]{2} x^{2} - 8$

(xi) $\frac{1}{2 x^{2}}$

(xii) $\frac{1}{\sqrt{5}} x^{\frac{1}{2}} + 1$

(xiii) $\frac{3}{5} x^{2} - \frac{7}{3} x + 9$

(xiv) $x^{4} - x^{\frac{3}{2}} + x - 3$

(xv) $2 x^{3} + 3 x^{2} + \sqrt{x} - 1$

Which of the following is not a polynomial ?

(a) $\sqrt{3} x^{2} - 2 \sqrt{3} x + 5$ (b) $9 x^{2} - 4 x + \sqrt{2}$

The polynomials $(2 x^{3} + x^{2} - a x + 2)$ and $(2 x^{3} - 3 x^{2} - 3 x + a)$ when divided by (x -2) leave the same remainder. Find the value of a.

Q. The polynomial

2 x^{3} + 13 x^{2} + x - 70

is exactly divisible by

x - 2

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