Question

From following which is a polynomial:

a. x⁻²+x+1

b. 2x⁰+1

c. x+1/x

d. x/2+3

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Answer 1

Answer:

Option B). 2x⁰ + 1

Explanation:

a). x⁻² + x + 1

Here, degree of x is -2 which isn't a whole number, so it can't be a polynomial.

b). 2x⁰ + 1

We know that, x⁰ = 1, so degree of x is 1. Hence it is a polynomial.

c). x + 1/x

Here, degree of x is -1 as 1/x = x-¹

So it can't be a polynomial.

d). x/2 + 3

Here, degree of x is not a whole number too, so it can't be a polynomial.

∴ Option B) 2x⁰ - 1 is correct.

Answer 2

Solution:

Options

1. a. x⁻²+x+1
2. b. 2x⁰+1
3. c. x+1/x
4. d. x/2+3

★ Concept :Polynomial is an expression which consists of only variables and constant terms , that involves four operations ( + , - , × , ÷ ) Addition , subtraction , multiplication & division & the of any term shouldn't be negative integer

Checking options

a) x⁻² + x + 1

Here , we can observe that x⁻² it has a negative integer . So , it cannot be a polynomial since , the concept

b) 2x⁰ + 1

We know that a⁰ = 1 similarly x⁰ = 1

Substituting we have

→ 2(1) + 1

→ 2 + 1

→ 3

Here , the power is nor negative nor positive . So, it can be considered as polynomial

c) x + 1/x

It can be written as

x + x⁻¹

Here, we have the same condition as we have in option. So, it cannot be considered.

d) x/2 + 3

It can be written as

x(2⁻¹) + 3

It has a negative integer - 1 . So , it cannot be considered

Hence , option b) 2x⁰ + 1 is right answer