Question

If 2x^a+3y^b+z^c+xyz is a polynomial then a^2+bc-c^2 cannot be equal to

Answer 1

Given that

2x^a+3y^b+z^c+xyz is a polynomial

Now according to the definition of a polynomial...

x , y , z are variables in the given polynomial

AND

a , b , c are their powers , so they must integers according to the definition of a polynomial.

Now  the other given expression a^2+bc-c^2 cannot be equal to a POLYNOMIAL because a , b & c all are constants. So the result of the expression a^2+bc-c^2 will also be a constant.

So a^2+bc-c^2 cannot be a Polynomial.

Answer 2

Given:

Polynomial : 2x^a + 3y^b + z^c + xyz

To find:

If 2x^a + 3y^b + z^c + xyz is a polynomial then a^2 + bc - c^2 cannot be equal to.

Solution:

By the definition of a polynomial,

The variables are exponent to the powers.

The powers are integers.

Here,

x, y, z are variables

a, b, c are their powers

Therefore,

a, b, c are integers.

In the other equation,

a, b, c are variables.

But, they are integers in the first equation

Hence, it cannot be a polynomial.

If 2x^a+3y^b+z^c+xyz is a polynomial then a^2+bc-c^2 cannot be equal to a polynomial.