Question

Is (4x² - 5/2x + 6)/x a polynomial? If not then state the reason ​

Answer 1

Answer:

NO

Step-by-step explanation:

Becuase t when we will bring x in numerator then it's power wlii become -1. Therefore it will not be polynomial

Answer 2

Concept to be used here:

• Remainder Theorem

Solving the Problem

• Quotient $\sf{4x^2-\dfrac{5}{2} x+6}$

• Dividend $\sf{x}$

It is not divisible.

After we substitute x=0,

we get 6 which is the remainder.

Hence we get a term $\sf{\dfrac{6}{x} }$ which is not a polynomial.

For your information.

To find the remainder, we substituted x=0.

Because we used the remainder theorem.

Like $\sf{\dfrac{6}{x} =6x^{-1}}$ or $\sf{\sqrt{x} =x^{\dfrac{1}{2} }}$, the terms in a negative exponent or fraction are not a polynomial.