Assertion (A) : Refer the following algebraic expression in terms of one variable : 3x + 9, 9 - $\dfrac{3}{\text{x}^2}$, 100.

Two of them are not polynomials in x.

Reason (R) : An algebraic expression is a polynomial if the power of each term used in it is a whole number.

1. Both A and R are correct, and R is the correct explanation for A.

2. Both A and R are correct, and R is not the correct explanation for A.

3. A is true, but R is false.

4. A is false, but R is true.

An algebraic expression is a polynomial if the power of each term used in it is a whole number.

So, reason (R) is true

A polynomial in one variable (say, x) must have:

• Only non-negative integers (i.e., whole numbers) as exponents of x.

• No negative or fractional powers.

So, reason (R) is true.

Given,

Algebraic expressions : 3x + 9, 9 - $\dfrac{3}{\text{x}^2}$, 100

3x + 9 and 100 (constant polynomial) both are polynomials, while 9 - $\dfrac{3}{\text{x}^2}$ is not as on taking the variable in numerator (9 - 3x^-2) the power becomes negative.

So, assertion (A) is false.

Hence, option 4 is the correct option.