What is the highest common factor (H.C.F.) of the polynomials 2x^2 + 4x and 4x^2 + 8x?

Answer: B. 4x
The H.C.F. of the polynomials 2x^2 + 4x and 4x^2 + 8x is 4x, as it is the highest degree polynomial that divides both without a remainder.