MCQ
Which of the following is a polynomial?
- A$2 x^2+\frac{3}{x}-5$
- B$-3 x^2+\sqrt{2 x}+4$
- ✓$\sqrt{2} x^3+\sqrt{3} x^2+\sqrt{5} x-3$
- D$\frac{5}{x^3}+2 x^2-3 x+\frac{1}{7}$
✓
Answer
Correct option: C.
$\sqrt{2} x^3+\sqrt{3} x^2+\sqrt{5} x-3$
(C) $\sqrt{2} x^3+\sqrt{3} x^2+\sqrt{5} x-3$
An expression of the form $a_0 x^n+a_1 x^{n-1}+a_2 x^{n-2}+\ldots+a_{n-1} x+a_n, a_0 \neq 0$ is a polynomial of degree $n$ (a natural number).
Clearly, in expression given in option (a) has a term containing $x^{-1}$. So, it is not a polynomial. Expression in option (b) has a term containing $x^{1 / 2}$, so it is not a polynomial. The expression in option (d) has a term containing $x^{-3}$, so it is not a polynomial. Expression in option (c) satisfies the definition of a polynomial.
An expression of the form $a_0 x^n+a_1 x^{n-1}+a_2 x^{n-2}+\ldots+a_{n-1} x+a_n, a_0 \neq 0$ is a polynomial of degree $n$ (a natural number).
Clearly, in expression given in option (a) has a term containing $x^{-1}$. So, it is not a polynomial. Expression in option (b) has a term containing $x^{1 / 2}$, so it is not a polynomial. The expression in option (d) has a term containing $x^{-3}$, so it is not a polynomial. Expression in option (c) satisfies the definition of a polynomial.
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