Which form of $p(x)=2x^3-8x$ most directly reveals all real zeros?

Answer and derivation

Correct answer: A

The factored form displays zeros $-2,0,2$.

1. $2x^3-8x=2x(x^2-4)$.
2. $x^2-4=(x-2)(x+2)$.
3. Each linear factor directly reveals one real zero.

Why the other options fail

A

Correct complete factorization.

B

It is equivalent but does not reveal the zeros directly.

C

The sign in the quadratic factor is wrong.

D

Expanding does not reproduce the polynomial.

Common misconception: Equivalent forms can be useful for different features; factored form is best for zeros.

China/AP bridge: AP questions often ask which form is useful, not merely whether algebraic manipulation is valid.