Which of the following does not represent a zero polynomial?

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p (x) = 0

p (x) = 0 . x^{0}

p (x) = x^{0} - 1

p (x) = x^{0}

answer is C.

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Detailed Solution

We need to find a polynomial who does not represent the zero polynomial.
Consider the polynomial,

p (x) = a x^{2} + bx + c

, which becomes a zero polynomial if

.
Therefore, a polynomial of zero can be expressed as

p (x) = 0

.
Although the coefficient of the polynomial

p (x) = x^{0}

p (x) = 1

is not equal to 0, it is not of the type

p (x) = 0,

because it is a constant polynomial.
Thus, the polynomial

p (x) = x^{0}

is not a zero polynomial
Hence, the correct option is 3.

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