Question

Which of the following is/are not polynomial(s)?

• A. $3$
• B. $4x^2+5\sqrt{x}$
• C. $\sqrt{3}{x}^3+x+1$
• D. $4x+5$

Answer 1

The correct option is B $4x^2+5\sqrt{x}$

For an expression to be a polynomial,
1) The coefficients must be real numbers
2) The exponents on the variable(s) must be whole numbers

3 can be written as $3\times x^0$. Since the coefficient (3) is a real number and the exponent (0) is a whole number, the expression is a polynomial.

$4x^2+5\sqrt{x}=4\times x^2+5\times x^{\frac{1}{2}}$. The coefficients, 4 and 5, are real numbers. Since $\frac{1}{2}$ is not a whole number, the expression is not a polynomial

In the expression $\sqrt{3}{x}^3+x+1$, the coefficients ($\sqrt{3}$,1 and 1) are real numbers and the exponents (3,1 and 0) are whole numbers. Thus, it is a polynomial.

The expression $4x+5$ is a polynomial as the coefficients (4 and 5) are real numbers and the exponents (1 and 0) are whole numbers