Which of the following is a cubic polynomial?

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Question

(B) polynomial is defined as an expression consisting of variables and coefficients,where the exponents of the variables must be non-negative integers

Vedclass · Accepted Answer

$p(x) = 2 - 3x - x^3$

Vedclass · Answer

(B) polynomial is defined as an expression consisting of variables and coefficients,where the exponents of the variables must be non-negative integers.$A$ cubic polynomial is a polynomial of degree $3$,meaning the highest power of the variable $x$ is $3$.In option $A$,the term $\sqrt{x}$ is $x^{1/2}$,which is not an integer.In option $B$,$p(x) = 2 - 3x - x^3$. The highest power of $x$ is $3$,and all exponents are non-negative integers. Thus,it is a cubic polynomial.In option $C$,$\sqrt{x^3} = x^{3/2}$,which is not an integer.In option $D$,the exponent $1/3$ is not an integer.Therefore,the correct option is $B$.

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