Think, Discuss and write which of the following expressions are polynomials? which are not? Give reasons. $(i) 4 x^{2} + 5 x - 2$
$(i i) y^{2}$
$(i i i) 5$
$(i v) 2 x^{2} + \frac{3}{x} - 5$

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Solution

$(i) 4 x^{2} + 5 x - 2 = 4 x^{2} + 5 x^{1} - 2 x^{0}$
Here power of the equation is $2, 1$ and $0$
Since all powers are whole number, it is a polynomial.
Now, since there is only one variable $x$ ,
it is a polynomial in one variable.

$(i i) y^{2}$
Here power of the equation is $2$
Since all powers are whole number, it is a polynomial.
Now, since there is only one variable $y$ ,
it is a polynomial in one variable.

$(i i i) 5 = 5 x^{0}$
Here power of the equation is $0$
Now, since there is only no variable or power of the variable is zero which is a whole number
it is a polynomial and known as constant polynomial.

$(i v) 2 x^{2} + \frac{3}{x} - 5 = 2 x^{2} + 3 x^{- 1} - 5 x^{0}$
Here power of the equation is $2, - 1$ and $0$
Since $- 1$ is not a whole number, it is not a polynomial.

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