Question

which of the following expression are polynomials . If not give reason:

1.) 1/x square + 3x-4

Not a polynomial one of the power of
x is negative
​

Answer 1

Answer:

Given expression is

$\frac{1}{x^2}+3x-4$

It can be written as

$x^{-2}+3x-4$

We know that a polynomial is an algebric expression of the form

$a_nx^n+a_{n-1}x^{n-1}+........+a_1x+a_0$

In this

$a_n, a_{n-1},...a_1, a_0$ are real numbers and $n, n-1, .....$ are whole numbers

Therefore, for an expression to be a polynomial, the power of the unknown i.e. x here, should be a whole number

Since in the given expression, the power of x is -2

Therefore, the given expression of not a polynomial

Hope this helps.