Which of the following statements is true?

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(A) polynomial of degree $n$ has at most $n$ zeros.For $A$: $p(x) = x^3 + 8$. This is a cubic polynomial (degree $3$),so it has $3$ zeros. Thus,this s

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$p(x) = x^3 + 8$ has three zeros.

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(A) polynomial of degree $n$ has at most $n$ zeros.For $A$: $p(x) = x^3 + 8$. This is a cubic polynomial (degree $3$),so it has $3$ zeros. Thus,this statement is true.For $B$: $p(x) = x^2 - 36$. This is a quadratic polynomial (degree $2$),so it has at most $2$ zeros. This statement is false.For $C$: $p(x) = 4x^3 + x = x(4x^2 + 1)$. The zeros are $x = 0$ and $4x^2 = -1$ (no real zeros). It has only $1$ real zero,though $3$ complex zeros. However,in the context of standard school mathematics,we often look for real roots. Even if we consider complex roots,$A$ is a more direct example of a cubic polynomial having $3$ roots.For $D$: $p(x) = 4x^3 - x = x(4x^2 - 1) = x(2x - 1)(2x + 1)$. The zeros are $x = 0, 1/2, -1/2$. This also has $3$ zeros.Note: Both $A, C,$ and $D$ have $3$ zeros. However,$p(x) = x^3 + 8$ is a standard cubic form. Given the options,$A$ is a correct statement.

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