Final answer:
The completely factored polynomial is option (a) 0. All other options provided can be factored further, such as 4(4x^4-1) that can be rewritten using the difference of squares.
Step-by-step explanation:
The student has asked which polynomial is factored completely. The polynomials provided are:
- (a) 0
- (b) 4(4x^4-1)
- (c) 2x^2(y^2 - 4y^2+5y)
- (d) 3x(9x^2 +1)
The completely factored polynomial is option (a) which is just 0, since 0 can be considered factored completely as it doesn't need any further simplification or factorization. All other options can still be factored more. For instance, option (b) can be factored further using the difference of squares formula, resulting in 4((2x^2)^2 - 1^2) which can be rewritten as 4(2x^2 + 1)(2x^2 - 1).