Question

Which algebraic expressions are polynomials? Check all that apply.

• A. $2x^3-\frac{1}{x}$
• B. $x^{3}y-3x^2+6x$
• C. $y^2+5y-\sqrt{3}$
• D. $2-\sqrt{4x}$
• E. $-x\sqrt{6}$
• F. $-\frac{1}{3}{x}^3-\frac{1}{2}{x}^2+\frac{1}{4}$

Answer 1

Answer: (B), (C), (E), (F)

$-\frac{1}{3}{x}^3-\frac{1}{2}{x}^2+\frac{1}{4}$

Explanation for correct options:

Identifying polynomials.

The algebraic expressions that contain the indices of variables as whole numbers and not negative integers or fractions are polynomials.

Option (B) :

The expression $x^{3}y-3x^2+6x$ has whole numbers as the exponents of variables. So, it is a polynomial.

Option (C) :

The expression $y^2+5y-\sqrt{3}$ has whole numbers as the exponents of variables. So, it is also a polynomial.

Option (E) :

The expression $-x\sqrt{6}$ has a whole number as the exponent of the variable. So, it is also a polynomial.

Option (F) :

The expression $-\frac{1}{3}{x}^3-\frac{1}{2}{x}^2+\frac{1}{4}$ has a whole number as the exponent of the variable. So, it is also a polynomial.

Explanation for in-correct options:

Option (A) :

The expression $2x^3-\frac{1}{x}$ can be written as $2x^3-x^{-1}$. So, it has a negative integer as the exponent of the variable. So, it is not a polynomial.

Option (D) :

The expression $2-\sqrt{4x}$ can be written as $2-2x^{\frac{1}{2}}$. So, it has a rational number, that is, $\frac{1}{2}$ as the exponent of the variable. So, it is not a polynomial.

Therefore, the option $\mathit{B}\mathbf{,}\mathit{C}\mathbf{,}\mathit{E}\mathbf{}\mathbf{and}\mathbf{}\mathit{F}$ are correct option.