Question

Which of the following does NOT represent a zero polynomial?

• A. $p\left(x\right)=0$
• B. $p\left(x\right)=0.x^0$
• C. $p\left(x\right)=x^0$
• D. $p\left(x\right)=x^0-1$

Answer 1

The correct option is C $p\left(x\right)=x^0$

Consider the polynomial, $p\left(x\right)=a{x}^2+bx+c$ , if $a=b=c=0$ then the expression becomes zero polynomial.

Therefore, the constant polynomial whose coefficients are all equal to $0$ is called a zero polynomial.

Zero polynomial can be written as $p\left(x\right)=0$.

Now, the polynomial $p\left(x\right)=x^0$ or $p\left(x\right)=1$ is a constant polynomial but the coefficient is not equal to $0$ and therefore it is not of the form $p\left(x\right)=0$.

Hence, the polynomial $p\left(x\right)=x^0$ is not a zero polynomial