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  • Which one of the following is a polynomial? A. x square divided 2 minus 2 divided x square B. square root 2x minus 1 C. x square plus 3x raies to 3 divided 2 divided square root of x

Which one of the following is a polynomial?  

(A) \frac{x^{2}}{2}-\frac{2}{x^{2}}\\ \\(B) \sqrt{2x}-1\\ \\(C)x^{2}+\frac{3x^{\frac{3}{2}}}{\sqrt{x}}\\ \\ (D)\frac{x-1}{x+2}

Answers (1)

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

Solution

            Polynomial: A polynomial is an expression consisting of variables and coefficients and also non negative powers. It contains different powers of the same variable,

            Here \frac{x^{2}}{2}-\frac{2}{x^{2}}  is not a polynomial because power of x must be a non-negative integer.

            \sqrt{2x}-1  is also not a polynomial because degree of variable should always be a whole number.

            x^{2}+\frac{3x^{\frac{3}{2}}}{\sqrt{x}}\Rightarrow x^{2}+3x^{\frac{3}{2}-\frac{1}{2}}\Rightarrow x^{2}+3x^{1}

            It is a polynomial because power of x is in whole numbers.

            \frac{x-1}{x+2}\Rightarrow \left ( x-1 \right )\left ( x+2 \right )^{-1}

            It is also not a polynomial because power of x is negative.

 

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