Question

Point out which of the following expressions are polynomials? Justify your answer.

• A. $6x^2-3x+1$
• B. $x^3-x^2+2x-2$
• C. $3x+\sqrt{x}-5$
• D. $\frac{1}{x^2}+\frac{1}{x}-7$
• E. $\sqrt{5}{x}^3+\frac{1}{3}x+4$
• F. $\frac{3}{x^2}+6$

Answer 1

Answer: (A), (B), (E)

$\sqrt{5}{x}^3+\frac{1}{3}x+4$

Explanation for correct answer:

The exponent of variable in each term of a polynomial expression should always be a whole number .

A) The exponents of variable in each term in the polynomial expression $6x^2-3x+1$ are $2,1$ and $0$. The numbers $2,1$ $0$ are whole numbers. Hence, it is a polynomial.

B) The exponents of variable in each term in the polynomial expression $x^3-x^2+2x-2$ are $3,2,1$ and $0$. The numbers $3,2,1$ and $0$ are whole numbers. Hence, it is a polynomial.

E) The exponents of variable in each term in the polynomial expression $\sqrt{5}{x}^3+\frac{1}{3}x+4$ are $3,1$ and $0$. The numbers $3,1$ and $0$ are whole numbers. Hence, it is a polynomial.

Explanation for incorrect answer:

C) The exponents of variable in each term in the polynomial expression $3x+\sqrt{x}-5$ are $1,\frac{1}{2}$ and $0$. The number $\frac{1}{2}$ is not a whole number. Hence, it is not a polynomial.

D) The exponents of variable in each term in the polynomial expression $\frac{1}{x^2}+\frac{1}{x}-7=x^{-2}+x^{-1}-7$ are $-2,-1$ and $0$. The numbers $-2$ and $-1$ are not whole numbers. Hence, it is not a polynomial.

F) The exponents of variable in each term in the polynomial expression $\frac{3}{x^2}+6=3x^{-2}+6$ are $-2$ and $0$. The numbers $-2$ is not a whole number. Hence, it is not a polynomial.

Hence, the correct options are option $\mathrm{A},\mathrm{B}$ and $\mathrm{E}$.