Question

which of the following expressions are polynomials? which are not ? Give reasons 1)4x^2+5x-2, 2)y^2-8, 3)5, 4)2x^2+3/x-5, 5)√3x^2+5x, 6)1/x+1, 7)1/√x, 8)3xyz​

Answer 1

Answer:

(i)4x

2

+5x−2=4x

2

+5x

1

−2x

0

Here power of the equation is 2,1 and 0

Since all powers are whole number, it is a polynomial.

Now, since there is only one variable x,

it is a polynomial in one variable.

(ii)y

2

Here power of the equation is 2

Since all powers are whole number, it is a polynomial.

Now, since there is only one variable y,

it is a polynomial in one variable.

(iii)5=5x

0

Here power of the equation is 0

Now, since there is only no variable or power of the variable is zero which is a whole number

it is a polynomial and known as constant polynomial.

(iv)2x

2

+

x

3

−5=2x

2

+3x

−1

−5x

0

Here power of the equation is 2,−1 and 0

Since −1 is not a whole number, it is not a polynomial.