Zach wants to factor 3x5−81x2. He knows that the difference of cubes formula is
a3−b3=(a−b)(a2+ab+b2).

Zach decides to use the formula. First, he factors 3x2 out of the expression. Next, he identifies a and b. Finally, he factors the expression according to the formula. His work is shown here.

3x5−81x2=3x2(x3−27)
a=x; b=3
3x5−81x2=3x2(x−3)(x2+3x+9)

Part A: Which statement correctly analyzes Zach’s work?

Part B: What is the correct factorization of the polynomial 3x5−81x2?